In this world:

I have a MATLAB assignment for Engineering Dynamics to work on and am having difficulty with some parts:

• In this world: the planar rigid body is a polygon with density density; the four springs have a stiffness of springStiffness; springRestLengths is a vector containing the four natural lengths of the four springs; and there's a function that returns the mass of the rigid body m and the moment of inertia about its center of gravity IG
• We have these global variables:
• m IG g local_corner_x local_corner_y
• FxInitial FyInitial MInitial initialForceDuration
• springAnchorPositions springRestLengths springStiffness springObjectAttachmentIndices

How would I setup the equations to calculate the derivatives of these 6 variables:

• the horizontal position of the center of the polygon?
• the vertical position of the center of the polygon?
• the angle of the polygon, in radians?
• the horizontal velocity of the center of the polygon, in meters per second?
• the vertical velocity of the center of the polygon, in meters per second?
• the angular velocity of the polygon, in radians per second?