From f37d791048705348ee76a09457cf47019c7ad70f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=D0=90=D1=80=D1=82=D1=91=D0=BC?= <111016733+ArkXo@users.noreply.github.com> Date: Tue, 11 Jun 2024 13:13:21 +0000 Subject: [PATCH 1/6] ftgy --- ark.py | 1 + 1 file changed, 1 insertion(+) create mode 100644 ark.py diff --git a/ark.py b/ark.py new file mode 100644 index 000000000..e75154b7c --- /dev/null +++ b/ark.py @@ -0,0 +1 @@ +print("hello world") \ No newline at end of file From 1fb2fffb9f7e4c4345c0086a043cda54bfb7516d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=D0=90=D1=80=D1=82=D1=91=D0=BC?= <111016733+ArkXo@users.noreply.github.com> Date: Tue, 11 Jun 2024 13:13:57 +0000 Subject: [PATCH 2/6] ff --- README.md | 3 --- 1 file changed, 3 deletions(-) delete mode 100644 README.md diff --git a/README.md b/README.md deleted file mode 100644 index f1ec59983..000000000 --- a/README.md +++ /dev/null @@ -1,3 +0,0 @@ -# Базовый курс (моделирование на python) -Репозиторий для прохождения базового курса по языку программирования python, -в рамках общего цикла лекций "Моделирование на python". From 83711c173cdad06b479ab720a1c20017d6351e5d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=D0=90=D1=80=D1=82=D1=91=D0=BC?= <111016733+ArkXo@users.noreply.github.com> Date: Fri, 14 Jun 2024 12:23:07 +0000 Subject: [PATCH 3/6] dd --- ark.py | 1 - 1 file changed, 1 deletion(-) delete mode 100644 ark.py diff --git a/ark.py b/ark.py deleted file mode 100644 index e75154b7c..000000000 --- a/ark.py +++ /dev/null @@ -1 +0,0 @@ -print("hello world") \ No newline at end of file From b1349c09d9d2146865c3221d95bb1623e771d8fa Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=D0=90=D1=80=D1=82=D1=91=D0=BC?= <111016733+ArkXo@users.noreply.github.com> Date: Sat, 15 Feb 2025 16:05:12 +0000 Subject: [PATCH 4/6] jkfjh --- lab_task1.py | 125 +++++++++++++++++++++++++++++++++++++ lab_task2.py | 132 +++++++++++++++++++++++++++++++++++++++ lab_task3.py | 125 +++++++++++++++++++++++++++++++++++++ lec1.py | 153 ++++++++++++++++++++++++++++++++++++++++++++++ lec_13_N_body.gif | Bin 0 -> 800227 bytes task1.gif | Bin 0 -> 1878342 bytes task2.gif | Bin 0 -> 1026238 bytes 7 files changed, 535 insertions(+) create mode 100644 lab_task1.py create mode 100644 lab_task2.py create mode 100644 lab_task3.py create mode 100644 lec1.py create mode 100644 lec_13_N_body.gif create mode 100644 task1.gif create mode 100644 task2.gif diff --git a/lab_task1.py b/lab_task1.py new file mode 100644 index 000000000..359c79051 --- /dev/null +++ b/lab_task1.py @@ -0,0 +1,125 @@ +import numpy as np +from scipy.integrate import odeint +import matplotlib.pyplot as plt +from matplotlib.animation import FuncAnimation + +# Определяем переменную величину +frames = 600 +seconds_in_year = 365 * 24 * 60 * 60 +years = 20 +t = np.linspace(0, years*seconds_in_year, frames) + +# Определяем функцию для системы диф. уравнений +def move_func(s, t): + (x1, v_x1, y1, v_y1, + x2, v_x2, y2, v_y2, + x3, v_x3, y3, v_y3) = s + + # Динамика первого тела под влиянием второго и третьего + dxdt1 = v_x1 + dv_xdt1 = ( + - G * m2 * (x1 - x2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + - G * m3 * (x1 - x3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + ) + dydt1 = v_y1 + dv_ydt1 = ( + - G * m2 * (y1 - y2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + - G * m2 * (y1 - y3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + ) + + # Динамика второго тела под влиянием первого и третьего + dxdt2 = v_x2 + dv_xdt2 = ( + - G * m1 * (x2 - x1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + - G * m3 * (x2 - x3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + ) + dydt2 = v_y2 + dv_ydt2 = ( + - G * m1 * (y2 - y1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + - G * m3 * (y2 - y3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + ) + + # Динамика третьего тела под влиянием второго и первого + dxdt3 = v_x3 + dv_xdt3 = ( + - G * m1 * (x3 - x1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + - G * m2 * (x3 - x2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + ) + dydt3 = v_y3 + dv_ydt3 = ( + - G * m1 * (y3 - y1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + - G * m2 * (y3 - y2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + ) + + return (dxdt1, dv_xdt1, dydt1, dv_ydt1, + dxdt2, dv_xdt2, dydt2, dv_ydt2, + dxdt3, dv_xdt3, dydt3, dv_ydt3) + +# Определяем начальные значения и параметры, +# входящие в систему диф. уравнений +x10 = -7.45 * 149 * 10**9 +v_x10 = 0 +y10 = 0 +v_y10 = -8435 + +x20 = 5.185 * 149 * 10**9 +v_x20 = 0 +y20 = 0 +v_y20 = 24556 + +x30 = 4.515 * 149 * 10**9 +v_x30 = 0 +y30 = 0 +v_y30 = -21893 + +s0 = (x10, v_x10, y10, v_y10, + x20, v_x20, y20, v_y20, + x30, v_x30, y30, v_y30) + +G = 6.67 * 10**(-11) +M_son = 1.989 * 10**30 + +m1 = 1.06 * M_son + +m2 = 0.96 * M_son + +m3 = 0.67 * M_son + +# Решаем систему диф. уравнений +sol = odeint(move_func, s0, t) + +# Строим решение в виде графика и анимируем +fig, ax = plt.subplots() + +balls = [] +balls_lines = [] + +for i in range(3): + balls.append(plt.plot([], [], 'o', color=f'C{i}')) + balls_lines.append(plt.plot([], [], '-', color=f'C{i}')) + +def animate(i): + for j in range(3): + balls[j][0].set_data([sol[i, 4*j]], [sol[i, 4*j+2]]) + balls_lines[j][0].set_data([sol[:i, 4*j]], [sol[:i, 4*j+2]]) + +ani = FuncAnimation(fig, animate, frames=frames, interval=30) + +plt.axis('equal') +edge = 1.8 * abs(x10) +ax.set_xlim(-edge, edge) +ax.set_ylim(-edge, edge) + +ani.save('task1.gif') \ No newline at end of file diff --git a/lab_task2.py b/lab_task2.py new file mode 100644 index 000000000..c05a574d8 --- /dev/null +++ b/lab_task2.py @@ -0,0 +1,132 @@ +import numpy as np +from scipy.integrate import odeint +import matplotlib.pyplot as plt +from matplotlib.animation import FuncAnimation + +# Определяем переменную величину +frames = 365 +seconds_in_year = 365 * 24 * 60 * 60 +seconds_in_day = 24 * 60 * 60 +years = 0.5 +t = np.linspace(0, years*seconds_in_year, frames) + +# Определяем функцию для системы диф. уравнений +def move_func(s, t): + (x1, v_x1, y1, v_y1, + x2, v_x2, y2, v_y2, + x3, v_x3, y3, v_y3) = s + + # Динамика первого тела под влиянием второго и третьего + dxdt1 = v_x1 + dv_xdt1 = ( + + k * q1 * q2 / m1 * (x1 - x2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + + k * q1 * q3 / m1 * (x1 - x3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + ) + dydt1 = v_y1 + dv_ydt1 = ( + + k * q1 * q2 / m1 * (y1 - y2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + + k * q1 * q3 / m1 * (y1 - y3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + ) + + # Динамика второго тела под влиянием первого и третьего + dxdt2 = v_x2 + dv_xdt2 = ( + + k * q2 * q1 / m2 * (x2 - x1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + + k * q2 * q3 / m2 * (x2 - x3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + ) + dydt2 = v_y2 + dv_ydt2 = ( + + k * q2 * q1 / m2 * (y2 - y1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + + k * q2 * q3 / m2 * (y2 - y3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + ) + + # Динамика третьего тела под влиянием второго и первого + dxdt3 = v_x3 + dv_xdt3 = ( + + k * q3 * q1 / m3 * (x3 - x1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + + k * q3 * q2 / m3 * (x3 - x2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + ) + dydt3 = v_y3 + dv_ydt3 = ( + + k * q3 * q1 / m3 * (y3 - y1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + + k * q3 * q2 / m3 * (y3 - y2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + ) + + return (dxdt1, dv_xdt1, dydt1, dv_ydt1, + dxdt2, dv_xdt2, dydt2, dv_ydt2, + dxdt3, dv_xdt3, dydt3, dv_ydt3) + +# Определяем начальные значения и параметры, +# входящие в систему диф. уравнений +k = 8.98755 * 10**9 +q = 2 * 10**5 +m = 1 +a = 149 * 10**9 +vx = 10**4 + +m1 = m +q1 = q + +m2 = m +q2 = q + +m3 = m +q3 = - q + +x10 = -a/2 +v_x10 = vx +y10 = - np.sin(np.pi/6) * a / 3 +v_y10 = 0 + +x20 = a/2 +v_x20 = -vx +y20 = - np.sin(np.pi/6) * a / 3 +v_y20 = 0 + +x30 = 0 +v_x30 = 0 +y30 = np.sin(np.pi/6) * a * 2 / 3 +v_y30 = 0 + +s0 = (x10, v_x10, y10, v_y10, + x20, v_x20, y20, v_y20, + x30, v_x30, y30, v_y30) + +# Решаем систему диф. уравнений +sol = odeint(move_func, s0, t) + +# Строим решение в виде графика и анимируем +fig, ax = plt.subplots() + +balls = [] +balls_lines = [] + +for i in range(3): + balls.append(plt.plot([], [], 'o', color=f'C{i}')) + balls_lines.append(plt.plot([], [], '-', color=f'C{i}')) + +def animate(i): + for j in range(3): + balls[j][0].set_data([sol[i, 4*j]], [sol[i, 4*j+2]]) + balls_lines[j][0].set_data([sol[:i, 4*j]], [sol[:i, 4*j+2]]) + +ani = FuncAnimation(fig, animate, frames=frames, interval=30) + +plt.axis('equal') +edge = 2 * abs(x10) +ax.set_xlim(-edge, edge) +ax.set_ylim(-edge, edge) + +ani.save('task2.gif') \ No newline at end of file diff --git a/lab_task3.py b/lab_task3.py new file mode 100644 index 000000000..832e6633a --- /dev/null +++ b/lab_task3.py @@ -0,0 +1,125 @@ +import numpy as np +from scipy.integrate import odeint +import matplotlib.pyplot as plt +from matplotlib.animation import FuncAnimation + +# Определяем переменную величину +frames = 600 +seconds_in_year = 365 * 24 * 60 * 60 +years = 20 +t = np.linspace(0, years*seconds_in_year, frames) + +# Определяем функцию для системы диф. уравнений +def move_func(s, t): + (x1, v_x1, y1, v_y1, + x2, v_x2, y2, v_y2, + x3, v_x3, y3, v_y3) = s + + # Динамика первого тела под влиянием второго и третьего + dxdt1 = v_x1 + dv_xdt1 = ( + - G * m2 * (x1 - x2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + - G * m3 * (x1 - x3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + ) + dydt1 = v_y1 + dv_ydt1 = ( + - G * m2 * (y1 - y2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + - G * m2 * (y1 - y3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + ) + + # Динамика второго тела под влиянием первого и третьего + dxdt2 = v_x2 + dv_xdt2 = ( + - G * m1 * (x2 - x1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + - G * m3 * (x2 - x3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + ) + dydt2 = v_y2 + dv_ydt2 = ( + - G * m1 * (y2 - y1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + - G * m3 * (y2 - y3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + ) + + # Динамика третьего тела под влиянием второго и первого + dxdt3 = v_x3 + dv_xdt3 = ( + - G * m1 * (x3 - x1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + - G * m2 * (x3 - x2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + ) + dydt3 = v_y3 + dv_ydt3 = ( + - G * m1 * (y3 - y1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + - G * m2 * (y3 - y2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + ) + + return (dxdt1, dv_xdt1, dydt1, dv_ydt1, + dxdt2, dv_xdt2, dydt2, dv_ydt2, + dxdt3, dv_xdt3, dydt3, dv_ydt3) + +# Определяем начальные значения и параметры, +# входящие в систему диф. уравнений +x10 = -7.45 * 149 * 10**9 +v_x10 = 0 +y10 = 0 +v_y10 = -8435 + +x20 = - 100 +v_x20 = 0 +y20 = 0 +v_y20 = 24556 + +x30 = 100 +v_x30 = 0 +y30 = 0 +v_y30 = -21893 + +s0 = (x10, v_x10, y10, v_y10, + x20, v_x20, y20, v_y20, + x30, v_x30, y30, v_y30) + +G = 6.67 * 10**(-11) +M_son = 1.989 * 10**30 + +m1 = 1.06 * M_son + +m2 = 0.96 * M_son + +m3 = 0.67 * M_son + +# Решаем систему диф. уравнений +sol = odeint(move_func, s0, t) + +# Строим решение в виде графика и анимируем +fig, ax = plt.subplots() + +balls = [] +balls_lines = [] + +for i in range(3): + balls.append(plt.plot([], [], 'o', color=f'C{i}')) + balls_lines.append(plt.plot([], [], '-', color=f'C{i}')) + +def animate(i): + for j in range(3): + balls[j][0].set_data([sol[i, 4*j]], [sol[i, 4*j+2]]) + balls_lines[j][0].set_data([sol[:i, 4*j]], [sol[:i, 4*j+2]]) + +ani = FuncAnimation(fig, animate, frames=frames, interval=30) + +plt.axis('equal') +edge = 1.8 * abs(x10) +ax.set_xlim(-edge, edge) +ax.set_ylim(-edge, edge) + +ani.save('task1.gif') \ No newline at end of file diff --git a/lec1.py b/lec1.py new file mode 100644 index 000000000..d3c6244c4 --- /dev/null +++ b/lec1.py @@ -0,0 +1,153 @@ +import numpy as np +from scipy.integrate import odeint +import matplotlib.pyplot as plt +from matplotlib.animation import FuncAnimation + +# Определяем переменную величину +frames = 365 +seconds_in_year = 365 * 24 * 60 * 60 +seconds_in_day = 24 * 60 * 60 +years = 0.5 +t = np.linspace(0, years*seconds_in_year, frames) + +# Определяем функцию для системы диф. уравнений +def move_func(s, t): + (x1, v_x1, y1, v_y1, + x2, v_x2, y2, v_y2, + x3, v_x3, y3, v_y3) = s + + # Динамика первого тела под влиянием второго и третьего + dxdt1 = v_x1 + dv_xdt1 = ( + - G * m2 * (x1 - x2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + - G * m3 * (x1 - x3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + + k * q1 * q2 / m1 * (x1 - x2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + + k * q1 * q3 / m1 * (x1 - x3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + ) + dydt1 = v_y1 + dv_ydt1 = ( + - G * m2 * (y1 - y2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + - G * m2 * (y1 - y3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + + k * q1 * q2 / m1 * (y1 - y2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + + k * q1 * q3 / m1 * (y1 - y3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + ) + + # Динамика второго тела под влиянием первого и третьего + dxdt2 = v_x2 + dv_xdt2 = ( + - G * m1 * (x2 - x1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + - G * m3 * (x2 - x3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + + k * q2 * q1 / m2 * (x2 - x1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + + k * q2 * q3 / m2 * (x2 - x3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + ) + dydt2 = v_y2 + dv_ydt2 = ( + - G * m1 * (y2 - y1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + - G * m3 * (y2 - y3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + + k * q2 * q1 / m2 * (y2 - y1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + + k * q2 * q3 / m2 * (y2 - y3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + ) + + # Динамика третьего тела под влиянием второго и первого + dxdt3 = v_x3 + dv_xdt3 = ( + - G * m1 * (x3 - x1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + - G * m2 * (x3 - x2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + + k * q3 * q1 / m3 * (x3 - x1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + + k * q3 * q2 / m3 * (x3 - x2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + ) + dydt3 = v_y3 + dv_ydt3 = ( + - G * m1 * (y3 - y1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + - G * m2 * (y3 - y2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + + k * q3 * q1 / m3 * (y3 - y1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + + k * q3 * q2 / m3 * (y3 - y2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + ) + + return (dxdt1, dv_xdt1, dydt1, dv_ydt1, + dxdt2, dv_xdt2, dydt2, dv_ydt2, + dxdt3, dv_xdt3, dydt3, dv_ydt3) + +# Определяем начальные значения и параметры, +# входящие в систему диф. уравнений +x10 = 149 * 10**9 +v_x10 = 0 +y10 = 0 +v_y10 = 30000 + +x20 = - 149 * 10**9 +v_x20 = 1 +y20 = 0 +v_y20 = - 30000 + +x30 = 0 +v_x30 = 15000 +y30 = 149 * 10**9 +v_y30 = 0 + +s0 = (x10, v_x10, y10, v_y10, + x20, v_x20, y20, v_y20, + x30, v_x30, y30, v_y30) + +m1 = 1.1 * 10**(30) +q1 = - 1.1 * 10**(20) + +m2 = 2.1 * 10**(30) +q2 = 2.1 * 10**(20) + +m3 = 3.6 * 10**(30) +q3 = - 3.1 * 10**(20) + +G = 6.67 * 10**(-11) +k = 8.98755 * 10**9 + +# Решаем систему диф. уравнений +sol = odeint(move_func, s0, t) + +# Строим решение в виде графика и анимируем +fig, ax = plt.subplots() + +balls = [] +balls_lines = [] + +for i in range(3): + balls.append(plt.plot([], [], 'o', color='r')) + balls_lines.append(plt.plot([], [], '-', color='r')) + +def animate(i): + for j in range(3): + balls[j][0].set_data([sol[i, 4*j]], [sol[i, 4*j+2]]) + balls_lines[j][0].set_data([sol[:i, 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z3L{9drcdwCLOhynwz%bOwV$RiU1>f(ovXXwuWYK{sF)&1)0H%W^id+?(!F4N+K%|Tfy&@}IoggB`i=iV0slqlhZC^= zA@rO1`}@eT&W=BXe)-Sd|0(oa8GHZ!>I#p9do`4Z;h%(lG^*Tdk#t73Yf+4EEB+Mv z{awI{6Z%!G$Md)Bt|vU|=iW#Znf+7f_fx=%6Z*-M@NA|kGyGNPr!BU(nW3x7vz57u z9)CdfkW9IY@)0*VAwCfm(OaPUTXZT&wV#GliKy4LBuQdTmW&_{|yWE{-Qq2$f5xp(Y5y4ILi_{Nb!Pr@yRT59C! z_37h7X$sj%ql7-UEe*jdr|ZeW-fqSkZR0fu(eiPUiwl0pBA^s{#H_zP+m|D3Mn`GF zP8^Y@@SujjF>HIP;q&?DznpY} zT!g8Q+SzIFA9ju3ry` Date: Sat, 22 Feb 2025 08:54:46 +0000 Subject: [PATCH 5/6] ijghih --- lab_task3.py | 69 +++++++++++++++++++++++++++++++++++++-------------- task3.gif | Bin 0 -> 4581 bytes 2 files changed, 50 insertions(+), 19 deletions(-) create mode 100644 task3.gif diff --git a/lab_task3.py b/lab_task3.py index 832e6633a..2140de17a 100644 --- a/lab_task3.py +++ b/lab_task3.py @@ -4,9 +4,10 @@ from matplotlib.animation import FuncAnimation # Определяем переменную величину -frames = 600 +frames = 365 seconds_in_year = 365 * 24 * 60 * 60 -years = 20 +seconds_in_day = 24 * 60 * 60 +years = 0.5 t = np.linspace(0, years*seconds_in_year, frames) # Определяем функцию для системы диф. уравнений @@ -22,6 +23,10 @@ def move_func(s, t): / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 - G * m3 * (x1 - x3) / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + + k * q1 * q2 / m1 * (x1 - x2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + + k * q1 * q3 / m1 * (x1 - x3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 ) dydt1 = v_y1 dv_ydt1 = ( @@ -29,6 +34,10 @@ def move_func(s, t): / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 - G * m2 * (y1 - y3) / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + + k * q1 * q2 / m1 * (y1 - y2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + + k * q1 * q3 / m1 * (y1 - y3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 ) # Динамика второго тела под влиянием первого и третьего @@ -38,6 +47,10 @@ def move_func(s, t): / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 - G * m3 * (x2 - x3) / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + + k * q2 * q1 / m2 * (x2 - x1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + + k * q2 * q3 / m2 * (x2 - x3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 ) dydt2 = v_y2 dv_ydt2 = ( @@ -45,6 +58,10 @@ def move_func(s, t): / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 - G * m3 * (y2 - y3) / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + + k * q2 * q1 / m2 * (y2 - y1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + + k * q2 * q3 / m2 * (y2 - y3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 ) # Динамика третьего тела под влиянием второго и первого @@ -54,6 +71,10 @@ def move_func(s, t): / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 - G * m2 * (x3 - x2) / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + + k * q3 * q1 / m3 * (x3 - x1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + + k * q3 * q2 / m3 * (x3 - x2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 ) dydt3 = v_y3 dv_ydt3 = ( @@ -61,6 +82,10 @@ def move_func(s, t): / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 - G * m2 * (y3 - y2) / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + + k * q3 * q1 / m3 * (y3 - y1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + + k * q3 * q2 / m3 * (y3 - y2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 ) return (dxdt1, dv_xdt1, dydt1, dv_ydt1, @@ -69,34 +94,40 @@ def move_func(s, t): # Определяем начальные значения и параметры, # входящие в систему диф. уравнений -x10 = -7.45 * 149 * 10**9 +G = 6.67 * 10**(-11) +k = 8.98755 * 10**9 +q = 10**(-20) +m = 1 +a = 100 + +m1 = ((5*k*(q**2))/(G*m) - m)/4 +q1 = q + +m2 = m +q2 = q + +m3 = m +q3 = q + +x10 = 0 v_x10 = 0 y10 = 0 -v_y10 = -8435 +v_y10 = 0 -x20 = - 100 +x20 = - a v_x20 = 0 y20 = 0 -v_y20 = 24556 +v_y20 = 0 -x30 = 100 +x30 = a v_x30 = 0 y30 = 0 -v_y30 = -21893 +v_y30 = 0 s0 = (x10, v_x10, y10, v_y10, x20, v_x20, y20, v_y20, x30, v_x30, y30, v_y30) -G = 6.67 * 10**(-11) -M_son = 1.989 * 10**30 - -m1 = 1.06 * M_son - -m2 = 0.96 * M_son - -m3 = 0.67 * M_son - # Решаем систему диф. уравнений sol = odeint(move_func, s0, t) @@ -118,8 +149,8 @@ def animate(i): ani = FuncAnimation(fig, animate, frames=frames, interval=30) plt.axis('equal') -edge = 1.8 * abs(x10) +edge = 2 * a ax.set_xlim(-edge, edge) ax.set_ylim(-edge, edge) -ani.save('task1.gif') \ No 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lab_task2.py => tasks/lab_task2.py | 0 lab_task3.py => tasks/lab_task3.py | 0 14 files changed, 884 insertions(+) create mode 100644 extratasks gifs/extratask1_a.gif create mode 100644 extratasks gifs/extratask1_b.gif create mode 100644 extratasks gifs/extratask1_c.gif create mode 100644 extratasks gifs/extratask1_d.gif create mode 100644 extratasks/lab_extratask1_a.py create mode 100644 extratasks/lab_extratask1_b.py create mode 100644 extratasks/lab_extratask1_c.py create mode 100644 extratasks/lab_extratask1_d.py rename task1.gif => tasks gifs/task1.gif (100%) rename task2.gif => tasks gifs/task2.gif (100%) rename task3.gif => tasks gifs/task3.gif (100%) rename lab_task1.py => tasks/lab_task1.py (100%) rename lab_task2.py => tasks/lab_task2.py (100%) rename lab_task3.py => tasks/lab_task3.py (100%) diff --git a/extratasks gifs/extratask1_a.gif b/extratasks gifs/extratask1_a.gif new file mode 100644 index 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zVZyhAdvAH41$2d(wXX~&2is2Ro3q^vrbZ%iEfUKcQGVmUf4uneiuuK-Gxqn|_Wa`6 zeC@?d>R@NCiq`8{5&*jGlO@)GqN_^;G~64Yi|)V&KwhD%tmY=1P<&7`|9)xL17 zwpiOQBF?2Tig@n(Mjv*dkY373L;8&~>rpzCszZyjxyKK-Z&A$=TIm8lahQ;kq5_aEn~)PvnNv;PCXEH%{t literal 0 HcmV?d00001 diff --git a/extratasks/lab_extratask1_a.py b/extratasks/lab_extratask1_a.py new file mode 100644 index 000000000..fba2af0aa --- /dev/null +++ b/extratasks/lab_extratask1_a.py @@ -0,0 +1,221 @@ +import numpy as np +from scipy.integrate import odeint +import matplotlib.pyplot as plt +from matplotlib.animation import FuncAnimation + +# Определяем переменную величину +frames = 50 +t = np.linspace(10**(-7), 1.5 * 10**(-7), 50*frames) + +# Определяем функцию для системы диф. уравнений +def move_func(s, t): + (x1, v_x1, y1, v_y1, + x2, v_x2, y2, v_y2, + x3, v_x3, y3, v_y3, + x4, v_x4, y4, v_y4) = s + + # Динамика первого тела под влиянием второго и третьего + dxdt1 = v_x1 + dv_xdt1 = ( + - G * m2 * (x1 - x2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + - G * m3 * (x1 - x3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + - G * m4 * (x1 - x4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + + k * q1 * q2 / m1 * (x1 - x2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + + k * q1 * q3 / m1 * (x1 - x3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + + k * q1 * q4 / m1 * (x1 - x4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + ) + dydt1 = v_y1 + dv_ydt1 = ( + - G * m2 * (y1 - y2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + - G * m2 * (y1 - y3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + - G * m4 * (y1 - y4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + + k * q1 * q2 / m1 * (y1 - y2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + + k * q1 * q3 / m1 * (y1 - y3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + + k * q1 * q4 / m1 * (y1 - y4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + ) + + # Динамика второго тела под влиянием первого и третьего + dxdt2 = v_x2 + dv_xdt2 = ( + - G * m1 * (x2 - x1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + - G * m3 * (x2 - x3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + - G * m4 * (x2 - x4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + + k * q2 * q1 / m2 * (x2 - x1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + + k * q2 * q3 / m2 * (x2 - x3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + + k * q2 * q4 / m2 * (x2 - x4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + ) + dydt2 = v_y2 + dv_ydt2 = ( + - G * m1 * (y2 - y1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + - G * m3 * (y2 - y3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + - G * m4 * (y2 - y4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + + k * q2 * q1 / m2 * (y2 - y1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + + k * q2 * q3 / m2 * (y2 - y3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + + k * q2 * q4 / m2 * (y2 - y4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + ) + + # Динамика третьего тела под влиянием второго и первого + dxdt3 = v_x3 + dv_xdt3 = ( + - G * m1 * (x3 - x1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + - G * m2 * (x3 - x2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + - G * m4 * (x3 - x4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + + k * q3 * q1 / m3 * (x3 - x1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + + k * q3 * q2 / m3 * (x3 - x2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + + k * q3 * q4 / m3 * (x3 - x4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + ) + dydt3 = v_y3 + dv_ydt3 = ( + - G * m1 * (y3 - y1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + - G * m2 * (y3 - y2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + - G * m4 * (y3 - y4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + + k * q3 * q1 / m3 * (y3 - y1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + + k * q3 * q2 / m3 * (y3 - y2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + + k * q3 * q4 / m3 * (y3 - y4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + ) + + dxdt4 = v_x4 + dv_xdt4 = ( + - G * m1 * (x4 - x1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + - G * m2 * (x4 - x2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + - G * m3 * (x4 - x3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + + k * q4 * q1 / m4 * (x4 - x1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + + k * q4 * q2 / m4 * (x4 - x2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + + k * q4 * q3 / m4 * (x4 - x3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + ) + dydt4 = v_y4 + dv_ydt4 = ( + - G * m1 * (y4 - y1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + - G * m2 * (y4 - y2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + - G * m3 * (y4 - y3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + + k * q4 * q1 / m4 * (y4 - y1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + + k * q4 * q2 / m4 * (y4 - y2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + + k * q4 * q3 / m4 * (y4 - y3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + ) + + return (dxdt1, dv_xdt1, dydt1, dv_ydt1, + dxdt2, dv_xdt2, dydt2, dv_ydt2, + dxdt3, dv_xdt3, dydt3, dv_ydt3, + dxdt4, dv_xdt4, dydt4, dv_ydt4) + +# Определяем начальные значения и параметры, +# входящие в систему диф. уравнений +G = 6.67 * 10**(-11) +k = 8.98755 * 10**9 +q = 1.1 *10**(-13) +m = 1.1 * 10**(-27) +a = 0.008 +v = 4 * 10**7 +alpha = np.pi/4 + +m1 = m +q1 = -q + +m2 = m +q2 = q + +m3 = m +q3 = - q + +m4 = m +q4 = q + +x10 = a +v_x10 = - v * np.cos(alpha) +y10 = a +v_y10 = v * np.sin(alpha) + +x20 = a +v_x20 = v * np.cos(alpha) +y20 = - a +v_y20 = v * np.sin(alpha) + +x30 = - a +v_x30 = v * np.cos(alpha) +y30 = - a +v_y30 = - v * np.cos(alpha) + +x40 = - a +v_x40 = - v * np.cos(alpha) +y40 = a +v_y40 = - v * np.cos(alpha) + +s0 = (x10, v_x10, y10, v_y10, + x20, v_x20, y20, v_y20, + x30, v_x30, y30, v_y30, + x40, v_x40, y40, v_y40) + +# Решаем систему диф. уравнений +sol = odeint(move_func, s0, t) + +# Строим решение в виде графика и анимируем +fig, ax = plt.subplots() + +balls = [] +balls_lines = [] + +for i in range(4): + balls.append(plt.plot([], [], 'o', color=f'C{i}')) + balls_lines.append(plt.plot([], [], '-', color=f'C{i}')) + +def animate(i): + for j in range(4): + balls[j][0].set_data([sol[i, 4*j]], [sol[i, 4*j+2]]) + balls_lines[j][0].set_data([sol[:i, 4*j]], [sol[:i, 4*j+2]]) + +ani = FuncAnimation(fig, animate, frames=frames, interval=70) + +plt.axis('equal') +edge = 5 * a +ax.set_xlim(-edge, edge) +ax.set_ylim(-edge, edge) + +ani.save('extratask1_a.gif') \ No newline at end of file diff --git a/extratasks/lab_extratask1_b.py b/extratasks/lab_extratask1_b.py new file mode 100644 index 000000000..9c3988832 --- /dev/null +++ b/extratasks/lab_extratask1_b.py @@ -0,0 +1,221 @@ +import numpy as np +from scipy.integrate import odeint +import matplotlib.pyplot as plt +from matplotlib.animation import FuncAnimation + +# Определяем переменную величину +frames = 50 +t = np.linspace(10**(-7), 1.5 * 10**(-7), 50*frames) + +# Определяем функцию для системы диф. уравнений +def move_func(s, t): + (x1, v_x1, y1, v_y1, + x2, v_x2, y2, v_y2, + x3, v_x3, y3, v_y3, + x4, v_x4, y4, v_y4) = s + + # Динамика первого тела под влиянием второго и третьего + dxdt1 = v_x1 + dv_xdt1 = ( + - G * m2 * (x1 - x2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + - G * m3 * (x1 - x3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + - G * m4 * (x1 - x4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + + k * q1 * q2 / m1 * (x1 - x2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + + k * q1 * q3 / m1 * (x1 - x3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + + k * q1 * q4 / m1 * (x1 - x4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + ) + dydt1 = v_y1 + dv_ydt1 = ( + - G * m2 * (y1 - y2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + - G * m2 * (y1 - y3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + - G * m4 * (y1 - y4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + + k * q1 * q2 / m1 * (y1 - y2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + + k * q1 * q3 / m1 * (y1 - y3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + + k * q1 * q4 / m1 * (y1 - y4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + ) + + # Динамика второго тела под влиянием первого и третьего + dxdt2 = v_x2 + dv_xdt2 = ( + - G * m1 * (x2 - x1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + - G * m3 * (x2 - x3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + - G * m4 * (x2 - x4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + + k * q2 * q1 / m2 * (x2 - x1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + + k * q2 * q3 / m2 * (x2 - x3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + + k * q2 * q4 / m2 * (x2 - x4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + ) + dydt2 = v_y2 + dv_ydt2 = ( + - G * m1 * (y2 - y1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + - G * m3 * (y2 - y3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + - G * m4 * (y2 - y4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + + k * q2 * q1 / m2 * (y2 - y1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + + k * q2 * q3 / m2 * (y2 - y3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + + k * q2 * q4 / m2 * (y2 - y4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + ) + + # Динамика третьего тела под влиянием второго и первого + dxdt3 = v_x3 + dv_xdt3 = ( + - G * m1 * (x3 - x1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + - G * m2 * (x3 - x2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + - G * m4 * (x3 - x4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + + k * q3 * q1 / m3 * (x3 - x1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + + k * q3 * q2 / m3 * (x3 - x2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + + k * q3 * q4 / m3 * (x3 - x4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + ) + dydt3 = v_y3 + dv_ydt3 = ( + - G * m1 * (y3 - y1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + - G * m2 * (y3 - y2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + - G * m4 * (y3 - y4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + + k * q3 * q1 / m3 * (y3 - y1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + + k * q3 * q2 / m3 * (y3 - y2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + + k * q3 * q4 / m3 * (y3 - y4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + ) + + dxdt4 = v_x4 + dv_xdt4 = ( + - G * m1 * (x4 - x1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + - G * m2 * (x4 - x2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + - G * m3 * (x4 - x3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + + k * q4 * q1 / m4 * (x4 - x1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + + k * q4 * q2 / m4 * (x4 - x2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + + k * q4 * q3 / m4 * (x4 - x3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + ) + dydt4 = v_y4 + dv_ydt4 = ( + - G * m1 * (y4 - y1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + - G * m2 * (y4 - y2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + - G * m3 * (y4 - y3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + + k * q4 * q1 / m4 * (y4 - y1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + + k * q4 * q2 / m4 * (y4 - y2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + + k * q4 * q3 / m4 * (y4 - y3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + ) + + return (dxdt1, dv_xdt1, dydt1, dv_ydt1, + dxdt2, dv_xdt2, dydt2, dv_ydt2, + dxdt3, dv_xdt3, dydt3, dv_ydt3, + dxdt4, dv_xdt4, dydt4, dv_ydt4) + +# Определяем начальные значения и параметры, +# входящие в систему диф. уравнений +G = 6.67 * 10**(-11) +k = 8.98755 * 10**9 +q = 1.1 *10**(-13) +m = 1.1 * 10**(-27) +a = 0.008 +v = 3 * 10**7 +alpha = np.pi/4 + +m1 = m +q1 = -q + +m2 = m +q2 = q + +m3 = m +q3 = - q + +m4 = m +q4 = q + +x10 = a +v_x10 = - v * np.cos(alpha) +y10 = a +v_y10 = v * np.sin(alpha) + +x20 = a +v_x20 = v * np.cos(alpha) +y20 = - a +v_y20 = v * np.sin(alpha) + +x30 = - a +v_x30 = v * np.cos(alpha) +y30 = - a +v_y30 = - v * np.cos(alpha) + +x40 = - a +v_x40 = - v * np.cos(alpha) +y40 = a +v_y40 = - v * np.cos(alpha) + +s0 = (x10, v_x10, y10, v_y10, + x20, v_x20, y20, v_y20, + x30, v_x30, y30, v_y30, + x40, v_x40, y40, v_y40) + +# Решаем систему диф. уравнений +sol = odeint(move_func, s0, t) + +# Строим решение в виде графика и анимируем +fig, ax = plt.subplots() + +balls = [] +balls_lines = [] + +for i in range(4): + balls.append(plt.plot([], [], 'o', color=f'C{i}')) + balls_lines.append(plt.plot([], [], '-', color=f'C{i}')) + +def animate(i): + for j in range(4): + balls[j][0].set_data([sol[i, 4*j]], [sol[i, 4*j+2]]) + balls_lines[j][0].set_data([sol[:i, 4*j]], [sol[:i, 4*j+2]]) + +ani = FuncAnimation(fig, animate, frames=frames, interval=70) + +plt.axis('equal') +edge = 5 * a +ax.set_xlim(-edge, edge) +ax.set_ylim(-edge, edge) + +ani.save('extratask1_b.gif') \ No newline at end of file diff --git a/extratasks/lab_extratask1_c.py b/extratasks/lab_extratask1_c.py new file mode 100644 index 000000000..5455238e6 --- /dev/null +++ b/extratasks/lab_extratask1_c.py @@ -0,0 +1,221 @@ +import numpy as np +from scipy.integrate import odeint +import matplotlib.pyplot as plt +from matplotlib.animation import FuncAnimation + +# Определяем переменную величину +frames = 50 +t = np.linspace(10**(-7), 1.5 * 10**(-7), 50*frames) + +# Определяем функцию для системы диф. уравнений +def move_func(s, t): + (x1, v_x1, y1, v_y1, + x2, v_x2, y2, v_y2, + x3, v_x3, y3, v_y3, + x4, v_x4, y4, v_y4) = s + + # Динамика первого тела под влиянием второго и третьего + dxdt1 = v_x1 + dv_xdt1 = ( + - G * m2 * (x1 - x2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + - G * m3 * (x1 - x3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + - G * m4 * (x1 - x4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + + k * q1 * q2 / m1 * (x1 - x2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + + k * q1 * q3 / m1 * (x1 - x3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + + k * q1 * q4 / m1 * (x1 - x4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + ) + dydt1 = v_y1 + dv_ydt1 = ( + - G * m2 * (y1 - y2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + - G * m2 * (y1 - y3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + - G * m4 * (y1 - y4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + + k * q1 * q2 / m1 * (y1 - y2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + + k * q1 * q3 / m1 * (y1 - y3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + + k * q1 * q4 / m1 * (y1 - y4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + ) + + # Динамика второго тела под влиянием первого и третьего + dxdt2 = v_x2 + dv_xdt2 = ( + - G * m1 * (x2 - x1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + - G * m3 * (x2 - x3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + - G * m4 * (x2 - x4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + + k * q2 * q1 / m2 * (x2 - x1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + + k * q2 * q3 / m2 * (x2 - x3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + + k * q2 * q4 / m2 * (x2 - x4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + ) + dydt2 = v_y2 + dv_ydt2 = ( + - G * m1 * (y2 - y1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + - G * m3 * (y2 - y3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + - G * m4 * (y2 - y4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + + k * q2 * q1 / m2 * (y2 - y1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + + k * q2 * q3 / m2 * (y2 - y3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + + k * q2 * q4 / m2 * (y2 - y4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + ) + + # Динамика третьего тела под влиянием второго и первого + dxdt3 = v_x3 + dv_xdt3 = ( + - G * m1 * (x3 - x1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + - G * m2 * (x3 - x2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + - G * m4 * (x3 - x4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + + k * q3 * q1 / m3 * (x3 - x1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + + k * q3 * q2 / m3 * (x3 - x2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + + k * q3 * q4 / m3 * (x3 - x4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + ) + dydt3 = v_y3 + dv_ydt3 = ( + - G * m1 * (y3 - y1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + - G * m2 * (y3 - y2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + - G * m4 * (y3 - y4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + + k * q3 * q1 / m3 * (y3 - y1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + + k * q3 * q2 / m3 * (y3 - y2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + + k * q3 * q4 / m3 * (y3 - y4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + ) + + dxdt4 = v_x4 + dv_xdt4 = ( + - G * m1 * (x4 - x1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + - G * m2 * (x4 - x2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + - G * m3 * (x4 - x3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + + k * q4 * q1 / m4 * (x4 - x1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + + k * q4 * q2 / m4 * (x4 - x2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + + k * q4 * q3 / m4 * (x4 - x3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + ) + dydt4 = v_y4 + dv_ydt4 = ( + - G * m1 * (y4 - y1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + - G * m2 * (y4 - y2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + - G * m3 * (y4 - y3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + + k * q4 * q1 / m4 * (y4 - y1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + + k * q4 * q2 / m4 * (y4 - y2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + + k * q4 * q3 / m4 * (y4 - y3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + ) + + return (dxdt1, dv_xdt1, dydt1, dv_ydt1, + dxdt2, dv_xdt2, dydt2, dv_ydt2, + dxdt3, dv_xdt3, dydt3, dv_ydt3, + dxdt4, dv_xdt4, dydt4, dv_ydt4) + +# Определяем начальные значения и параметры, +# входящие в систему диф. уравнений +G = 6.67 * 10**(-11) +k = 8.98755 * 10**9 +q = 1.1 *10**(-13) +m = 1.1 * 10**(-27) +a = 0.008 +v = 2 * 10**7 +alpha = np.pi/4 + +m1 = m +q1 = -q + +m2 = m +q2 = q + +m3 = m +q3 = - q + +m4 = m +q4 = q + +x10 = a +v_x10 = - v * np.cos(alpha) +y10 = a +v_y10 = v * np.sin(alpha) + +x20 = a +v_x20 = v * np.cos(alpha) +y20 = - a +v_y20 = v * np.sin(alpha) + +x30 = - a +v_x30 = v * np.cos(alpha) +y30 = - a +v_y30 = - v * np.cos(alpha) + +x40 = - a +v_x40 = - v * np.cos(alpha) +y40 = a +v_y40 = - v * np.cos(alpha) + +s0 = (x10, v_x10, y10, v_y10, + x20, v_x20, y20, v_y20, + x30, v_x30, y30, v_y30, + x40, v_x40, y40, v_y40) + +# Решаем систему диф. уравнений +sol = odeint(move_func, s0, t) + +# Строим решение в виде графика и анимируем +fig, ax = plt.subplots() + +balls = [] +balls_lines = [] + +for i in range(4): + balls.append(plt.plot([], [], 'o', color=f'C{i}')) + balls_lines.append(plt.plot([], [], '-', color=f'C{i}')) + +def animate(i): + for j in range(4): + balls[j][0].set_data([sol[i, 4*j]], [sol[i, 4*j+2]]) + balls_lines[j][0].set_data([sol[:i, 4*j]], [sol[:i, 4*j+2]]) + +ani = FuncAnimation(fig, animate, frames=frames, interval=70) + +plt.axis('equal') +edge = 5 * a +ax.set_xlim(-edge, edge) +ax.set_ylim(-edge, edge) + +ani.save('extratask1_c.gif') \ No newline at end of file diff --git a/extratasks/lab_extratask1_d.py b/extratasks/lab_extratask1_d.py new file mode 100644 index 000000000..1f94891f1 --- /dev/null +++ b/extratasks/lab_extratask1_d.py @@ -0,0 +1,221 @@ +import numpy as np +from scipy.integrate import odeint +import matplotlib.pyplot as plt +from matplotlib.animation import FuncAnimation + +# Определяем переменную величину +frames = 50 +t = np.linspace(10**(-7), 1.5 * 10**(-7), 50*frames) + +# Определяем функцию для системы диф. уравнений +def move_func(s, t): + (x1, v_x1, y1, v_y1, + x2, v_x2, y2, v_y2, + x3, v_x3, y3, v_y3, + x4, v_x4, y4, v_y4) = s + + # Динамика первого тела под влиянием второго и третьего + dxdt1 = v_x1 + dv_xdt1 = ( + - G * m2 * (x1 - x2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + - G * m3 * (x1 - x3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + - G * m4 * (x1 - x4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + + k * q1 * q2 / m1 * (x1 - x2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + + k * q1 * q3 / m1 * (x1 - x3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + + k * q1 * q4 / m1 * (x1 - x4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + ) + dydt1 = v_y1 + dv_ydt1 = ( + - G * m2 * (y1 - y2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + - G * m2 * (y1 - y3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + - G * m4 * (y1 - y4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + + k * q1 * q2 / m1 * (y1 - y2) + / ((x1 - x2)**2 + (y1 - y2)**2)**1.5 + + k * q1 * q3 / m1 * (y1 - y3) + / ((x1 - x3)**2 + (y1 - y3)**2)**1.5 + + k * q1 * q4 / m1 * (y1 - y4) + / ((x1 - x4)**2 + (y1 - y4)**2)**1.5 + ) + + # Динамика второго тела под влиянием первого и третьего + dxdt2 = v_x2 + dv_xdt2 = ( + - G * m1 * (x2 - x1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + - G * m3 * (x2 - x3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + - G * m4 * (x2 - x4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + + k * q2 * q1 / m2 * (x2 - x1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + + k * q2 * q3 / m2 * (x2 - x3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + + k * q2 * q4 / m2 * (x2 - x4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + ) + dydt2 = v_y2 + dv_ydt2 = ( + - G * m1 * (y2 - y1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + - G * m3 * (y2 - y3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + - G * m4 * (y2 - y4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + + k * q2 * q1 / m2 * (y2 - y1) + / ((x2 - x1)**2 + (y2 - y1)**2)**1.5 + + k * q2 * q3 / m2 * (y2 - y3) + / ((x2 - x3)**2 + (y2 - y3)**2)**1.5 + + k * q2 * q4 / m2 * (y2 - y4) + / ((x2 - x4)**2 + (y2 - y4)**2)**1.5 + ) + + # Динамика третьего тела под влиянием второго и первого + dxdt3 = v_x3 + dv_xdt3 = ( + - G * m1 * (x3 - x1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + - G * m2 * (x3 - x2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + - G * m4 * (x3 - x4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + + k * q3 * q1 / m3 * (x3 - x1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + + k * q3 * q2 / m3 * (x3 - x2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + + k * q3 * q4 / m3 * (x3 - x4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + ) + dydt3 = v_y3 + dv_ydt3 = ( + - G * m1 * (y3 - y1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + - G * m2 * (y3 - y2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + - G * m4 * (y3 - y4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + + k * q3 * q1 / m3 * (y3 - y1) + / ((x3 - x1)**2 + (y3 - y1)**2)**1.5 + + k * q3 * q2 / m3 * (y3 - y2) + / ((x3 - x2)**2 + (y3 - y2)**2)**1.5 + + k * q3 * q4 / m3 * (y3 - y4) + / ((x3 - x4)**2 + (y3 - y4)**2)**1.5 + ) + + dxdt4 = v_x4 + dv_xdt4 = ( + - G * m1 * (x4 - x1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + - G * m2 * (x4 - x2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + - G * m3 * (x4 - x3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + + k * q4 * q1 / m4 * (x4 - x1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + + k * q4 * q2 / m4 * (x4 - x2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + + k * q4 * q3 / m4 * (x4 - x3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + ) + dydt4 = v_y4 + dv_ydt4 = ( + - G * m1 * (y4 - y1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + - G * m2 * (y4 - y2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + - G * m3 * (y4 - y3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + + k * q4 * q1 / m4 * (y4 - y1) + / ((x4 - x1)**2 + (y4 - y1)**2)**1.5 + + k * q4 * q2 / m4 * (y4 - y2) + / ((x4 - x2)**2 + (y4 - y2)**2)**1.5 + + k * q4 * q3 / m4 * (y4 - y3) + / ((x4 - x3)**2 + (y4 - y3)**2)**1.5 + ) + + return (dxdt1, dv_xdt1, dydt1, dv_ydt1, + dxdt2, dv_xdt2, dydt2, dv_ydt2, + dxdt3, dv_xdt3, dydt3, dv_ydt3, + dxdt4, dv_xdt4, dydt4, dv_ydt4) + +# Определяем начальные значения и параметры, +# входящие в систему диф. уравнений +G = 6.67 * 10**(-11) +k = 8.98755 * 10**9 +q = 1.1 *10**(-13) +m = 1.1 * 10**(-27) +a = 0.008 +v = 1 * 10**7 +alpha = np.pi/4 + +m1 = m +q1 = -q + +m2 = m +q2 = q + +m3 = m +q3 = - q + +m4 = m +q4 = q + +x10 = a +v_x10 = - v * np.cos(alpha) +y10 = a +v_y10 = v * np.sin(alpha) + +x20 = a +v_x20 = v * np.cos(alpha) +y20 = - a +v_y20 = v * np.sin(alpha) + +x30 = - a +v_x30 = v * np.cos(alpha) +y30 = - a +v_y30 = - v * np.cos(alpha) + +x40 = - a +v_x40 = - v * np.cos(alpha) +y40 = a +v_y40 = - v * np.cos(alpha) + +s0 = (x10, v_x10, y10, v_y10, + x20, v_x20, y20, v_y20, + x30, v_x30, y30, v_y30, + x40, v_x40, y40, v_y40) + +# Решаем систему диф. уравнений +sol = odeint(move_func, s0, t) + +# Строим решение в виде графика и анимируем +fig, ax = plt.subplots() + +balls = [] +balls_lines = [] + +for i in range(4): + balls.append(plt.plot([], [], 'o', color=f'C{i}')) + balls_lines.append(plt.plot([], [], '-', color=f'C{i}')) + +def animate(i): + for j in range(4): + balls[j][0].set_data([sol[i, 4*j]], [sol[i, 4*j+2]]) + balls_lines[j][0].set_data([sol[:i, 4*j]], [sol[:i, 4*j+2]]) + +ani = FuncAnimation(fig, animate, frames=frames, interval=70) + +plt.axis('equal') +edge = 5 * a +ax.set_xlim(-edge, edge) +ax.set_ylim(-edge, edge) + +ani.save('extratask1_d.gif') \ No newline at end of file diff --git a/task1.gif b/tasks gifs/task1.gif similarity index 100% rename from task1.gif rename to tasks gifs/task1.gif diff --git a/task2.gif b/tasks gifs/task2.gif similarity index 100% rename from task2.gif rename to tasks gifs/task2.gif diff --git a/task3.gif b/tasks gifs/task3.gif similarity index 100% rename from task3.gif rename to tasks gifs/task3.gif diff --git a/lab_task1.py b/tasks/lab_task1.py similarity index 100% rename from lab_task1.py rename to tasks/lab_task1.py diff --git a/lab_task2.py b/tasks/lab_task2.py similarity index 100% rename from lab_task2.py rename to tasks/lab_task2.py diff --git a/lab_task3.py b/tasks/lab_task3.py similarity index 100% rename from lab_task3.py rename to tasks/lab_task3.py

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