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


by vladgrigore
Tags: euler, ode, pitch, roll, yaw
vladgrigore
vladgrigore is offline
#1
Oct28-11, 02:26 PM
P: 3
Hello,

I am trying for a couple of hours now to integrate these equations ( http://en.wikipedia.org/wiki/Euler%2...dy_dynamics%29 ) 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, im 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
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