Structure and Interpretation of Classical Mechanics

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A bead of mass *m* moves without friction on a triaxial ellipsoidal surface. In rectangular coordinates the surface satisfies

for some constants *a*, *b*, and *c*. Identify suitable generalized coordinates, formulate a Lagrangian, and find Lagrange’s equations.

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[guess]

The generalized coordinates:

where

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(define theta (literal-function 'theta)) (define phi (literal-function 'phi)) ; (define (x t) (* 'a (sin (theta t)) (cos (phi t)))) ((D x) 't) (show-expression ((D x) 't)) ; (define (y t) (* 'b (sin (theta t)) (sin (phi t)))) (show-expression (y 't)) ((D y) 't) (show-expression ((D y) 't))

[guess]

— Me@2021-02-16 07:20:25 AM

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