Structure and Interpretation of Classical Mechanics

.

Use the procedure Gamma-bar to construct a procedure that transforms velocities given a coordinate transformation. Apply this procedure to the procedure p->r to deduce (again) equation (1.65).

~~~

(define ((Gamma-bar f-bar) path-q-local-tuple)
  (let* ((tqva path-q-local-tuple)
         (t (time tqva))         
         (O-tqva (osculating-path tqva)))   
    ((f-bar O-tqva) t)))

(define (F->C F)
  (define (f-bar q-prime)
    (define q
      (compose F (Gamma q-prime)))
    (Gamma q))
  (Gamma-bar f-bar))

(define (F->v F)
  (compose velocity (F->C F)))

(show-expression 
 ((F->v p->r)
  (->local 't
           (up 'r 'theta)
           (up 'rdot 'thetadot))))

— Me@2024-09-13 07:17:24 PM

.

.

2024.09.13 Friday (c) All rights reserved by ACHK