Mechanics in Differential GeometryWalter de Gruyter, 2006 - 571 من الصفحات This course and reference book is autonomous and is based on differential geometry in a practical way with symplectic geometry as a tool. Didactic comparisons, diagrams, exercises highlight modern mechanics. Principles, canonical forms, perturbations, stability, qualitative dynamics, and more precede an original Fourier transforms method. |
المحتوى
Chapter | 1 |
Chapter | 2 |
Dual space | 3 |
Symmetric and antisymmetric tensors | 17 |
1 | 25 |
2 | 31 |
3 | 40 |
2 | 53 |
EXERCISES | 234 |
2 | 262 |
4 | 274 |
A MODERN EXPOSITION OF MECHANICS | 285 |
3 | 295 |
5 | 302 |
38 | 330 |
COMPARISON OF THE LAGRANGIAN AND HAMILTONIAN | 334 |
1 | 60 |
2 | 68 |
21 | 74 |
COTANGENT BUNDLE AND COVECTOR FIELDS | 75 |
3 | 82 |
2 | 88 |
6 | 94 |
2 | 103 |
3 | 112 |
4 | 118 |
2 | 130 |
Lie derivative of tensor fields of type | 143 |
4 | 151 |
6 | 161 |
Pullback and integral evaluation | 175 |
Poincaré lemma | 183 |
2 | 213 |
HAMILTONJACOBI MECHANICS | 370 |
INTRODUCTION TO PERTURBATIONS | 409 |
Small motions about a critical point and Lagranian equations | 412 |
3 | 429 |
4 | 439 |
EXERCISES | 460 |
Chapter 4 | 481 |
23 | 492 |
42 | 508 |
53 | 517 |
2223 | 523 |
66 | 529 |
73 | 547 |
BIBLIOGRAPHY | 553 |
| 564 | |
| 571 | |
طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
algebra associated basis bracket bundle called canonical transformation chart closed complete components conclude condition constant coordinates corresponding deduce defined definition denoted diffeomorphism differential form element equality equations equivalent example exists expressed exterior function Given going Hamilton Hamiltonian immediately implies integral integral curve introduce known Lagrange Lagrangian Let us consider Lie derivative linear manifold mapping matrix mechanics motion namely neighborhood obtained orbit orientable p-form P₁ particular phase space position principle problem Proof proposition prove reader recall Remark respect solution space structure symplectic tangent vector tensor tensor of type theorem variables variational vector field vector space written X₁ zero ән да др