By Kurt Sundermeyer (auth.)

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14) ~E exists and is unique. a chart and thereby d e m o n s t r a t e Euler-Lagrange equations. 14) implements one already formalism. 15) and recalling (4. 17) yields ~L. 1~) w~a ~-- w~ d . 20) allow for the conclusion . ~0) W ~ ~ being the elements of are indeed the Euler-Lagrange In the hyperregular push-forward related by ~E be solved uniquely with the result W -4 . 21) these for a regular Lagrangian. FL gives is a diffeomorphism, ~U , and H and the L are II. C L A S S I C A L S I N G U L A R SYSTEMS W i t h the e x c e p t i o n of sect.

Is q u a s i - i n v a r i a n t t w ~ ÷ ~ , under the former trans- f o r m a t i o n s the c o r r e s p o n d i n g g e n e r a t o r for i n f i n i t e s i m a l c a n o n i c a l t r a n s f o r m a t i o n s becomes Here it is m e a n t that the q w h i c h is p o s s i b l e 4. G e o m e t r i c a l 91 -- are e x p r e s s e d as functions of p and in the regular case. f o r m u l a t i o n of c l a s s i c a l d y n a m i c s In the f o l l o w i n g we w i l l try to clarify the g e o m e t r i c a l structure of the objects d e s c r i b e d in c o o r d i n a t e language in p r e v i o u s sections.

W r i t t e n in c o o r d i n a t e language. - All of these sections are So it is u n d e r s t o o d that all statements and c a l c u l a t i o n s hold locally in certain u n s p e c i f i e d neighborhoods. 5. A l r e a d y in the i n t r o d u c t i o n Dynamics" it was m e n t i o n e d that " C o n s t r a i n e d is of little r e l e v a n c e to point mechanics. For n o n r e l a t i v i s t i c c l a s s i c a l m e c h a n i c s one has to c o n s t r u c t a r t i f i c i a l e x a m p l e s of the type c o n s i d e r e d in sect.

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