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; mostly typing these up to confirm that they display as expected
(define ((Gamma w) t)
(up t (w t) ((D w) t)))
(define ((Lagrange-equations Lagrangian) w)
(- (D (compose ((partial 2) Lagrangian) (Gamma w)))
(compose ((partial 1) Lagrangian) (Gamma w))))
(define ((L-harmonic m k) local)
(let ((q (coordinate local))
(v (velocity local)))
(- (* 1/2 m (square v))
(* 1/2 k (square q)))))
(define (proposed-solution t)
(* 'a (cos (+ (* 'omega t) 'phi))))
(show-expression
(((Lagrange-equations (L-harmonic 'm 'k))
proposed-solution)
't))
; didn't simplify the way The Book shows it, but is equivalent
(show-expression
(((Lagrange-equations (L-harmonic 'm 'k))
(literal-function 'x))
't))
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