Geometric Mechanics, Issue 1798Geometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters are written in the spirit of Newtonian Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications. |
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Contents
I | 1 |
II | 3 |
III | 4 |
IV | 7 |
V | 8 |
VI | 9 |
VIII | 11 |
IX | 12 |
XL | 140 |
XLI | 142 |
XLII | 145 |
XLIV | 147 |
XLV | 150 |
XLVI | 153 |
XLVII | 155 |
XLVIII | 162 |
X | 13 |
XI | 16 |
XII | 20 |
XIII | 23 |
XIV | 25 |
XV | 29 |
XVI | 34 |
XVII | 36 |
XVIII | 50 |
XIX | 55 |
XX | 60 |
XXI | 61 |
XXII | 63 |
XXIII | 66 |
XXIV | 68 |
XXV | 70 |
XXVI | 78 |
XXVII | 102 |
XXVIII | 107 |
XXIX | 111 |
XXX | 119 |
XXXI | 123 |
XXXIII | 127 |
XXXIV | 133 |
XXXV | 135 |
XXXVI | 136 |
XXXVIII | 137 |
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Common terms and phrases
affine associated Assume basis called complex components compute condition connection consider constant constraints contained coordinates corresponding curvature curve defined definition denote depend derivative diffeomorphism differentiable dissipative distribution element energy equal equations equivalent Example Exercise exists expression fact fixed flow forces function geodesic given gives implies induced integral introduced invariant isometry light linear Lorentz manifold mass means measure mechanical system metric motion neighborhood null vector observer obtain operator orientable orthogonal orthonormal particle positive projection Proof Proposition prove regular relative Remark represented respect result Riemannian rigid body rotation satisfies Show smooth solution space space-time special relativity stationary structure submanifold tangent tangent vector tensor field theorem Theory transformation unique vector field write zero
Bibliographic information
| Title | Geometric Mechanics, Issue 1798 Geometric Mechanics, Waldyr M. Oliva Volume 1798 of Lecture Notes in Mathematics Lecture notes in mathematics Berlin: Mathematical biosciences subseries |
| Author | Waldyr M. Oliva |
| Edition | illustrated |
| Publisher | Springer Science & Business Media, 2002 |
| ISBN | 3540442421, 9783540442424 |
| Length | 270 pages |
| Subjects | › › Mathematics / Geometry / Differential Mathematics / Linear & Nonlinear Programming Mathematics / Mathematical Analysis Science / Physics / General Science / Physics / Mathematical & Computational |
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