Structure and Interpretation of Classical Mechanics
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b. Use your delta
procedure to verify the properties of listed in exercise 1.7 for simple functions such as implemented by the procedure
f
:
(define (f q) (compose (literal-function ’F (-> (UP Real (UP* Real) (UP* Real)) Real)) (Gamma q)))
This implements an n-degree-of-freedom path-dependent function that depends on the local tuple of the path at each moment. You can define a literal two-dimensional path by
(define q (literal-function ’q (-> Real (UP Real Real))))
You should compute both sides of the equalities and subtract the results. The answer should be zero.
~~~
(define (((delta eta) f) q) (define (g epsilon) (f (+ q (* epsilon eta)))) ((D g) 0)) (define (f q) (compose (literal-function 'f (-> (UP Real Real Real) Real)) (Gamma q))) (define eta (literal-function 'eta)) (define q (literal-function 'q)) (print-expression ((((delta eta) f) q) 't))
— Patrick Eli Catach
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(print-expression ((((delta eta) f) q) 't))
(+ (* ((D eta) t) (((partial 2) f) (up t (q t) ((D q) t)))) (* (eta t) (((partial 1) f) (up t (q t) ((D q) t)))))
(show-expression ((((delta eta) f) q) 't))
— Me@2020-04-11 12:01:04 PM
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2020.04.11 Saturday (c) All rights reserved by ACHK
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