- #1
vladgrigore
- 3
- 0
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: [itex]\dot{f}[/itex]=[itex]\partial{f}[/itex]/[itex]\partial{t}[/itex][itex]\cong[/itex][itex]\Delta[/itex]f/[itex]\Delta[/itex]t=(f(t+[itex]\Delta[/itex]t)-f(t))/[itex]\Delta[/itex]t .
I am trying to do this, because I'm hoping to use the integration algorithm to find the Euler's Angles ([itex]\phi[/itex], [itex]\theta[/itex], [itex]\psi[/itex]) 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
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: [itex]\dot{f}[/itex]=[itex]\partial{f}[/itex]/[itex]\partial{t}[/itex][itex]\cong[/itex][itex]\Delta[/itex]f/[itex]\Delta[/itex]t=(f(t+[itex]\Delta[/itex]t)-f(t))/[itex]\Delta[/itex]t .
I am trying to do this, because I'm hoping to use the integration algorithm to find the Euler's Angles ([itex]\phi[/itex], [itex]\theta[/itex], [itex]\psi[/itex]) 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