我正在编写飞机模拟，为什么我的计算变得不稳定？

Question

I am currently attempting to code a basic 2D simulation of an airplane's flight (computing acceleration, speed and position at each timestep).

I have finally achieved a satisfactory simulation but now I face a new problem : After a period of time my computations start to become instable and quickly diverge towards infinity. Example of instability .

I have done some experiments and it seems that the higher the theta (angle between the ground and the axis of the plane) the later the instability comes (or does not even come). However, for realistic results I need to be able to compute with values of theta between -15 and +15 degrees.

I think this might be due to the approximations made by Python regarding small values. I have tried to use Decimals but the problem was the same.

Here is the link to the code : https://github.com/YannBerthelot/PlaneModel/blob/master/Plane-Env/env/FlightModel_2.py

Does anyone have an idea on how I can suppress or at least greatly reduce instability (making it happen after a much longer number of timesteps)? The problem may come from a wrong definition of the dynamics, if you have ideas on how to improve it please share :)

Thank you

Answer 1

Without any code it is not possible to find out exactly what is wrong. It is likely that you are using trigonometric functions like "tan" with inut values that yield values close to infinity - in this case even the smallest error in the way computers deal with numbers (not a Python peculiarity) will multiply enormously

In [15]: math.tan(math.pi/2 - 0.000001)                                                                                                             
Out[15]: 1000000.000020701

In [16]: math.tan(math.pi/2 - 0.000002)                                                                                                             
Out[16]: 499999.99996964744

What you have to do is to identify in your formula where is that you are getting these runaway values, and solve it symbolically, getting to an equivalent formula that won't need to calculate numeric results at these regions.

Then, the standard float precision of ~15 decimal places should more than suffice.