Analytical Mechanics

Front Cover
Springer Science & Business Media, Mar 26, 2002 - Computers - 864 pages
According to established tradition, courses on analytical mechanics include general equations of motion of holonomic and non-holonomic systems, vari ational principles, theory of canonical transformations, canonical equations and theory of their integration (the Hamilton-Jacobi theorem), integral in variants, theory of last multiplier and others. The fundamental laws of mechanics are taken for granted and are not subject to discussion. The present book is concerned with those issues of the above listed sub jects which, in the author's opinion, are most closely related to engineering problems. Application of the methods of analytical mechanics to non-trivial prob lems at the very stage of constructing the equations requires detailed knowl edge of the issues that are normally only briefly touched upon. With this perspective considerable attention is paid to ways of introducing the gener alised coordinates, the theory of finite rotation, methods of calculating the kinetic energy, the energy of accelerations, the potential energy of forces of various nature, and the resisting forces. These introductory chapters, which have to some extent independent significance, are followed by those on methods of constructing differential equations of motion for holonomic and non-holonomic systems in various forms. In these chapters the issues of their interrelations, determination of the constraint forces and some prob lems of analytical statics are discussed as well. It is thought useful to include geometric considerations of the motion of a material system as motion of the representative point in Riemannian space.
 

Contents

IV
19
V
21
VI
25
VII
28
VIII
30
IX
34
X
36
XI
39
CXXXV
387
CXXXVI
391
CXXXVII
395
CXXXIX
398
CXL
400
CXLI
402
CXLII
408
CXLIII
415

XII
40
XIII
42
XIV
47
XVII
50
XVIII
51
XIX
54
XX
60
XXI
62
XXII
64
XXIII
67
XXIV
71
XXV
72
XXVI
74
XXVII
76
XXVIII
79
XXX
81
XXXI
83
XXXII
87
XXXIII
88
XXXIV
91
XXXV
93
XXXVI
102
XXXVII
105
XXXVIII
111
XXXIX
114
XL
117
XLI
122
XLIII
124
XLIV
125
XLV
127
XLVI
129
XLVII
130
XLVIII
133
XLIX
138
L
139
LI
142
LII
146
LIII
151
LIV
155
LV
158
LVI
162
LVII
164
LVIII
167
LIX
170
LX
172
LXI
174
LXII
176
LXIII
180
LXIV
183
LXV
184
LXVI
185
LXVII
188
LXVIII
191
LXIX
193
LXXI
194
LXXII
196
LXXIII
203
LXXIV
205
LXXV
208
LXXVI
214
LXXVII
216
LXXVIII
221
LXXIX
227
LXXX
231
LXXXII
234
LXXXIII
238
LXXXIV
242
LXXXV
245
LXXXVI
247
LXXXVII
248
LXXXVIII
252
LXXXIX
254
XC
260
XCI
267
XCII
271
XCIII
272
XCIV
275
XCV
278
XCVI
281
XCVIII
283
XCIX
286
C
288
CI
291
CII
292
CIII
296
CIV
303
CV
307
CVI
309
CVII
310
CVIII
312
CIX
316
CX
319
CXI
321
CXII
324
CXIII
325
CXIV
326
CXV
329
CXVII
331
CXVIII
334
CXIX
339
CXX
341
CXXI
343
CXXII
346
CXXIII
349
CXXIV
353
CXXV
356
CXXVI
358
CXXVII
363
CXXVIII
364
CXXIX
367
CXXX
370
CXXXI
373
CXXXII
377
CXXXIII
379
CXXXIV
383
CXLIV
418
CXLV
421
CXLVI
425
CL
426
CLI
428
CLII
429
CLIII
434
CLIV
436
CLV
443
CLVI
449
CLVII
456
CLVIII
459
CLIX
462
CLX
468
CLXI
475
CLXII
483
CLXIII
484
CLXIV
486
CLXV
490
CLXVI
492
CLXVII
498
CLXVIII
506
CLXIX
512
CLXX
515
CLXXI
523
CLXXII
526
CLXXIII
531
CLXXIV
532
CLXXV
533
CLXXVI
536
CLXXVII
537
CLXXVIII
541
CLXXIX
543
CLXXX
546
CLXXXI
550
CLXXXII
552
CLXXXIII
553
CLXXXIV
554
CLXXXV
557
CLXXXVI
560
CLXXXVII
566
CLXXXVIII
567
CLXXXIX
568
CXC
569
CXCI
571
CXCII
574
CXCIII
576
CXCIV
585
CXCV
589
CXCVI
590
CXCVII
598
CXCVIII
599
CXCIX
605
CC
611
CCI
621
CCII
625
CCIII
631
CCIV
634
CCV
637
CCVI
642
CCVII
649
CCVIII
652
CCIX
657
CCX
660
CCXI
661
CCXIII
665
CCXIV
669
CCXV
671
CCXVI
676
CCXVII
692
CCXVIII
698
CCXX
707
CCXXI
710
CCXXII
714
CCXXIII
723
CCXXV
726
CCXXVI
727
CCXXVII
729
CCXXVIII
733
CCXXIX
735
CCXXX
739
CCXXXI
742
CCXXXII
747
CCXXXIII
753
CCXXXIV
756
CCXXXV
757
CCXXXVI
760
CCXXXVII
761
CCXXXVIII
765
CCXXXIX
770
CCXL
772
CCXLI
776
CCXLII
781
CCXLIII
786
CCXLIV
794
CCXLV
801
CCXLVI
802
CCXLVII
805
CCXLVIII
808
CCXLIX
810
CCL
811
CCLI
814
CCLII
818
CCLIII
819
CCLIV
823
CCLV
825
CCLVI
828
CCLVII
833
CCLVIII
836
CCLIX
838
CCLX
845
CCLXI
849
CCLXII
857
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