Question

I was reading Herbert Goldstein's Classical Mechanics. Its first chapter explains holonomic and non-holonomic constraints, but I still don’t understand the underlying concept. Can anyone explain it to me in detail and in simple language?

Options:
A) Holonomic constraints involve only the coordinates and time explicitly in the constraints equations.
B) Non-holonomic constraints involve only the velocities and time explicitly in the constraints equations.
C) Holonomic constraints restrict the possible motions of a system, but the constraints can be integrated without involving velocities explicitly.
D) Non-holonomic constraints involve both the coordinates and velocities explicitly in the constraint equations.

Answer 1

Holonomic constraints involve only the coordinates and time explicitly in the constraint equations and can be integrated without involving velocities explicitly. Non-holonomic constraints involve both the coordinates and velocities explicitly in the constraint equations.

Step-by-step explanation:

In classical mechanics, holonomic and non-holonomic constraints are used to describe the restrictions on the possible motions of a system.

Holonomic constraints involve only the coordinates and time explicitly in the constraint equations. They can be integrated without involving velocities explicitly. For example, a constraint that restricts a particle to move on a plane can be described by the equation f(x, y, t) = 0.

Non-holonomic constraints, on the other hand, involve both the coordinates and velocities explicitly in the constraint equations. For example, a constraint that restricts the velocity of a particle to a specific direction can be described by the equation g(x, y, dx/dt, dy/dt, t) = 0.