The Theoretical Minimum: What You Need to Know to Start Doing Physics by George Hrabovsky

Author:George Hrabovsky [Hrabovsky, George]
Language: eng
Format: azw3
ISBN: 9780141976235
Publisher: Penguin Books Ltd
Published: 2013-01-28T16:00:00+00:00

This looks exactly like Newton’s equations with centrifugal and Coriolis forces. Notice that there is something new in the form of the force law. The components of the Coriolis force,

depend not only on the position of the particle but also on its velocity. The Coriolis force is a velocity-dependent force.

Exercise 3: Use the Euler-Lagrange equations to derive the equations of motion from this Lagrangian.

The main point of this exercise was not so much to derive the centrifugal and Coriolis forces as to show you how to transform a mechanics problem from one coordinate system to another by simply rewriting the Lagrangian in the new coordinates. This is, by far, the easiest way to do the transformation—a lot easier than trying to transform Newton’s equations directly.

Another example, which we will leave to you, is to transform George’s equations to polar coordinates:

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