Solving an ordinary differential equation including a rotation matrix

I would like to solve the following first order ODEs in MATLAB:

R_dot = R*u_hat;
P_dot = R*v;
m_dot = m*u_hat + n*v + l
n_dot = n*u_hat + f;

With states:

R, P, m, n

I am familiar with Matlab's ode45 solver and have used it before, but on vectors only.

However, I was wondering if this could be applied on rotation matrices such as R.

Keeping in mind that R must remain orthonormal and:

inv(R) = R'

Thanks!

Answer 1

[Omar Alahmad]

I found the solution to be in chapter 6 of the Technical Report of Oliver J. Woodman, "An introduction to inertial navigation".

I simply implemented my own ODE solver for that.

Regards,

Omar

Answer 2

[Bruno Luong]

Might be you should rewrite ODE with the rotation not in term of 3x3 matrix but euler-rotation vector 3x1, then you should not worry much about constraint violation due to integration.

[Omar Alahmad]

Hi Bruno Luong,

I found the solution to be in chapter 6 of the Technical Report of Oliver J. Woodman, "An introduction to inertial navigation".

I simply implemented my own ODE solver for that.

Regards,

Omar