Question

Take the wheels of a car to be ideal knife edges oriented parallel to the long axis of the car so that sideways motion is not permitted. "If the constraints imposed by the wheels were holonomic, parallel parking would be impossible." Please explain.

Answer 1

if the constraints are holonomic it implies that the constraints have a strict boundary. When the wheels are considered to be oriented parallel to the long axis of the car and it is such that sideways motion is not permitted, these constraints when made as holonomic also implies that the car can only move along the long axis of the car only and it cannot turn also, because turning will imply that one of the car's tires will be turning to create a curved path, which would imply that the particular wheel will be having some kind of slip (since it can move only in straight line), This is not possible if the constraints are holonomic. Since the turning itself is not allowed due to the Holonomic constraints, parallel parking would be impossible with these constraints.