Equations of Motion with Contact Forces

Consider an n-DOF dynamical system with a single frictional contact. The equation of motion of the systems in the matrix form can be written as [51, 52] 

Note that from the above definitions we have w = av for some constant a O. Let y e A be the vector of reduced generalized coordinates. From (3.11), we 

multiplying both sides of this equation by and solving for N give 

The reduced system (3.18) takes the form of (3.5). There is, however, one very important difference between the two systems the inertia matrix given by (3.19) is zero whenever A vanishes. 

Remark 3.1 For the case of a unilateral contact, (3.14) must be changed to 

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Equations of Motion with Contact Forces For this system, (3.4) takes the form... 

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