Analysis of the Holonomic Constraint in the Whipple Bicycle Model (P267)

In this work, we examine the holonomic constraint of the Whipple bicycle model on a level surface. In the Whipple model, one must enforce a constraint which ensures that the front and rear wheels touch the ground. We first derive the constraint in an intuitive geometric fashion and then verify that the constraint can be expressed as quartic polynomial in the sine of the frame pitch. We present three methods for enforcing the constraint in a dynamic model and comment on the differences and practical issues involved in each method.