Cross Products

Often a cross product is required in the application of dynamics of the equation of motions. This is especially true for the moment equations and their relationship to the angular rates.



I always preferred to follow the first form because I never need to remember the sign conventions. However in the next section on determinants it will be seen that the signs are laid out in an alternating pattern.

Principles for Building a Simple 3DOF Simulation

Remember to begin with Newton's laws.

First: a body at rest or moving straight will remain at rest or move straight if no unbalanced force is applied.

Second: A particle acted on by a force F has an acceleration a in the same direction and proportion to the force F.

Third: For every force acting on a particle, the particle exerts an equal and opposite reactive force.

These laws can be written into the equations of motion using these following forms:



Basically, the sum of forces is equal to mass time acceleration or the time rate of change of linear momentum. The sum of moments is equal to the sum of cross products of radius and force or the time rate of change of angular momentum. Knowing these few priciples and the appropriate form for the derivative of a vector in a rotating frame and applied the the time rate of change of angular momentum: