[英]Solving a system of first order differential equations and second order differential equations (Non-linear)
The problem问题
I currently have a system of four equations.我目前有一个由四个方程组成的系统。 Two are second-order differential equations and two are first-order differential equations:
两个是二阶微分方程,两个是一阶微分方程:
The initial conditions are:初始条件是:
x = 0 |
y = 0.3 |
f(x) = 2.05 |
f(y) = 0.55 |
All angles are in degrees.所有角度都以度为单位。
What I have tried我试过的
I have tried to use Google Colabs and worked with SciPy and NumPy.我曾尝试使用 Google Colab,并与 SciPy 和 NumPy 一起工作。 Unfortunately, I cannot figure out how to program it as these equations are non-linear.
不幸的是,我无法弄清楚如何对其进行编程,因为这些方程是非线性的。 Could somebody give me some tips on any other modules to use?
有人可以给我一些有关要使用的任何其他模块的提示吗?
Scipy has a Runge Kutta solver . Scipy 有一个Runge Kutta 求解器。 First, you have to transform your ODEs to first order system (you can always do that by setting z=y') and then try the RK solver.
首先,您必须将 ODE 转换为一阶系统(您始终可以通过设置 z=y' 来实现),然后尝试 RK 求解器。
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