Ex 1.19 A two-bar linkage, 2

Structure and Interpretation of Classical Mechanics

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… Formulate a Lagrangian that describes the system and find the Lagrange equations of motion …

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[guess]


(define ((U-rect g m1 m2 m3) local)
   (let* ((q (coordinate local))
 	 (y1 (ref q 1))
 	 (y2 (ref q 3))
 	 (y3 (ref q 5)))
     (* g (+ (* m1 y1)
	         (* m2 y2)
	         (* m3 y3)))))

;

(define (L-rect g m1 m2 m3)
  (- (T-rect m1 m2 m3) (U-rect g m1 m2 m3)))

(show-expression
 ((L-rect 'g 'm_1 'm_2 'm_3)
    (up 't
        (up 'x_1 'y_1 'x_2 'y_2 'x_3 'y_3)
        (up 'xdot_1 'ydot_1 'xdot_2 'ydot_2 'xdot_3 'ydot_3))))

;

(define (L-l l1 l2 g m_1 m_2 m_3)
  (compose
   (L-rect g m_1 m_2 m_3) (F->C (q->r l1 l2))))

(show-expression
 ((L-l 'l_1 'l_2 'g 'm_1 'm_2 'm_3)
  (->local 't
	       (up 'x_2 'y_2 'theta 'phi)
	       (up 'xdot_2 'ydot_2 'thetadot 'phidot))))

;

(show-expression
 (((Lagrange-equations
    (L-l 'l_1 'l_2 'g 'm_1 'm_2 'm_3))
   (up
    (literal-function 'x_2)
    (literal-function 'y_2)
    (literal-function 'theta)
    (literal-function 'phi)))
  't))

;

[guess]

— Me@2021-03-20 05:01:21 PM

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