Integrating Euler's equations for rigid body dynamics with Euler's Method

[vladgrigore]

Hello,

I am trying for a couple of hours now to integrate these equations ( http://en.wikipedia.org/wiki/Euler's_equations_(rigid_body_dynamics) ) with the Euler's method: $\dot{f}$=$\partial{f}$/$\partial{t}$$\cong$$\Delta$f/$\Delta$t=(f(t+$\Delta$t)-f(t))/$\Delta$t .

I am trying to do this, because I'm hoping to use the integration algorithm to find the Euler's Angles ($\phi$, $\theta$, $\psi$) so i can visually simulate the roll, pitch and yaw angles of an aircraft (i intend to do this with information received from a micro AHRS sensor with 3 accelerometers and 3 gyrometers). I know it's not the best approach because of the singularity and the 3x3 matrix with sin and cos.

Putting it all in one line, I am having problems transforming the equations in discrete time and I'm not sure if the components of the angular velocity vector ω after integration are exactly the roll,pitch and yaw that i need.

After the discretization i guess i`ll have a system with 3 differential equations that i will need to solve.

Any help is much appreciated, thank you

 

[jvicens]

!

Hello there,

As a fellow scientist, I understand your struggle with integrating these equations using the Euler's method. It can be a tricky process, especially when dealing with singularities and 3x3 matrices.

One approach you can take is to use a higher order integration method, such as the Runge-Kutta method, which can provide more accurate results. Additionally, you may want to consider using a numerical solver, like Matlab's ode45, which is specifically designed for solving systems of differential equations.

In terms of the components of the angular velocity vector, ω, after integration, they may not exactly correspond to the roll, pitch, and yaw angles you are looking for. It would be best to double check your equations and make sure they are in the correct form before proceeding with the integration.

I wish you the best of luck with your simulation and hope you are able to successfully integrate these equations. If you have any further questions, feel free to reach out. Good luck!