SciPy，微分方程错误的解决方案

Question

我创建了程序，该程序通过 this公式，使用matplotlib绘制了人体飞行路线图。该代码似乎是正确的，但是由于某些原因我得到了this，x和y为负，并且从某处出现在右上角。

我做了SciPy的this视频编码。

对于头等舱，一切都很好，因此，只看二等舱，后者必须计算此x和y坐标。

怎么了？谢谢。

from scipy import integrate
from math import sin, cos
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation

# constants:

g = 9.81

# input:

k = 0.05   # air resistance
angle = 60 # angle of throw
v0 = 5     # start velocity
m = 4      # mass of the body

class GraphTrajectoryAnimation:
    def __init__(self, x, y, color, m=1, lw=3, width=6, height=4, dpi=100):
        """
        Where x, y - NumPy lists with coordinates, color - color of line (default - choose by Random)
                        height, width, dpi - hw, dpi of the figure from PyLab.
        """
        self.figure = plt.figure(figsize=(width, height), dpi=dpi) # Init figure and his needs to plot 

        self.x = x
        self.y = y
        self.m = m
        self.color = color
        self.lw = lw

    def animation(self, i, x, y, m, color):
        """ Definition of a matplotlib animation. """
        plt.plot(x[:i * self.m], y[:i * self.m], lw=self.lw, color=self.color)

    def graph(self, interval=1):
        """ Definition of cycle FuncAnimation, which call animation. """
        self.graph_id = animation.FuncAnimation(self.figure, self.animation,
                                            fargs=(self.x, self.y, self.m, self.color),
                                            repeat=False, interval=interval)

    def showfigure(self):
        """ Call the graph function and displays it on the figure. """
        self.graph()
        plt.show()

class SolveSystemOfADifferentialEquations:
    def __init__(self, k, angle, v0, m):

        self.k = k
        self.angle = angle
        self.m = m
        self.v0 = v0
        self.v0_x = self.v0 * cos(self.angle)
        self.v0_y = self.v0 * sin(self.angle)
        self.kdivm = self.k / self.m
        self.time = np.linspace(0, 10, 100)

    def xmodel(self, X, t):
        x = X[0]
        dx = X[1]
        xdot = [ [], [] ]
        xdot[0] = dx
        xdot[1] = -self.kdivm * x
        return xdot

    def ymodel(self, Y, t):
        y = Y[0]
        dy = Y[1]
        ydot = [ [], [] ]
        ydot[0] = dy
        ydot[1] = -g - self.kdivm * dy
        return ydot

    def solveX(self):
        x = integrate.odeint(self.xmodel, [0, self.v0_x], self.time)
        return x

    def solveY(self):
        y = integrate.odeint(self.ymodel, [0, self.v0_y], self.time)
        return y

Solver = SolveSystemOfADifferentialEquations(k, angle, v0, m)
x = Solver.solveX()
y = Solver.solveY()

def show():
    root = GraphTrajectoryAnimation(x, y, 'blue')
    root.showfigure()

if __name__ == "__main__":
    show()

Answer 1

我认为这是因为您以度为单位给出角度，但是python中的sin和cos函数将其视为弧度。因此，当您编写sin（60）时，程序会考虑使用sin（60弧度）而不是sin（60度）。将π/ 3弧度而不是60度作为弹丸的初始角度，它应该可以工作。