By Hans Ziegler

ISBN-10: 0444865039

ISBN-13: 9780444865038

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N,odV+$t .. VjVjdA. n = \{i .. kL + t .. Vjj)dV. 52) for a n observer m o v i n g with the v o l u m e V. I n t h i s c a s e ( 2 . nVjVj dA. 53) T h i s is t h e c o n s e r v a t i o n c o n d i t i o n f r o m t h e p o i n t o f v i e w o f a n o b s e r v e r a t r e s t . I n f a c t , if A is i n t e r p r e t e d a s a s p a t i a l s u r f a c e , t h e i n t e g r a l o n t h e left is the increase of T j k n w i t h i n A p e r u n i t t i m e , a n d t h e r i g h t - h a n d s i d e is t h e supply from outside by flow t h r o u g h Eqs.

4 ) is e q u a l t o t h e lefth a n d s i d e o f ( 3 . 3 ) . T h u s , ( 3 . 3 ) is t h e a n a l y t i c a l f o r m o f t h e theorem linear momentum, formulated for the material b o d y V: t h e of material d e r i v a t i v e o f t h e l i n e a r m o m e n t u m is e q u a l t o t h e s u m o f t h e e x t e r n a l forces or, equivalently, t o the resultant force o b t a i n e d by r e d u c t i o n of the e x t e r n a l f o r c e s t o a n a r b i t r a r y p o i n t O. , for a r b i t r a r y systems of particles a n d rigid b o d i e s .

3) t h e s o l u t i o n is n o t u n i q u e . Problems 1. u) = φ - c u r i o - υ x g r a d φ. satisfied 24 2. Verify the identities d i v c u r l u i = 0, c u r l c u r l ν = g r a d d i v ν - A v. 3 . T h e i n s t a n t a n e o u s v e l o c i t y field Vi(x ) k a s Vj = i>,- + e a>jX 0) ijk of a rigid b o d y m a y b e written w h e r e i>/ a n d ω a r e c o n s t a n t v e c t o r s . S h o w t h a t t h e 0) ky ] d i v e r g e n c e o f t h e field is z e r o a n d t h a t its c u r l is 2 ω .

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An introduction to thermomechanics by Hans Ziegler


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