Structure and Interpretation of Classical Mechanics

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**b**. Write the formal Lagrangian

such that Lagrange’s equations will yield the Newton’s equations you derived in part a.

~~~

[guess]

(define (U-constraint q0 q1 F l) (* (/ F (* 2 l)) (- (square (- q1 q0)) (square l)))) (define ((extract-particle pieces) local i) (let* ((indices (apply up (iota pieces (* i pieces)))) (extract (lambda (tuple) (vector-map (lambda (i) (ref tuple i)) indices)))) (up (time local) (extract (coordinate local)) (extract (velocity local))))) (define q-rect (up (literal-function 'x_0) (literal-function 'y_0) (literal-function 'x_1) (literal-function 'y_1) (literal-function 'F))) (show-expression q-rect)

(show-expression (q-rect 't))

(show-expression (Gamma q-rect))

(show-expression ((Gamma q-rect) 'w))

(show-expression ((Gamma q-rect) 't))

(show-expression (time ((Gamma q-rect) 't)))

(show-expression (coordinate ((Gamma q-rect) 't)))

[guess]

— based on `/sicmutils/sicm-exercises`

— Me@2021-04-27 05:03:59 PM

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2021.04.28 Wednesday (c) All rights reserved by ACHK