| Edition |
First edition. |
| Description |
1 online resource (180 pages) : illustrations |
| Physical Medium |
polychrome |
| Description |
text file |
| Note |
Includes index. |
| Contents |
Cover; Contents; List of Figures; 1 The variational principle; 1.1 Euler-Lagrange equations; 1.2 The Variational principle of mechanics; 1.3 Deduction from quantum mechanics*; 2 Conservation laws; 2.1 Generalized momenta; 2.2 Conservation laws; 2.3 Conservation of energy; 2.4 Minimal surface of revolution; 3 The simple pendulum; 3.1 Algebraic formulation; 3.2 Primer on Jacobi functions; 3.3 Elliptic curves*; 3.4 Imaginary time; 3.5 The arithmetic-geometric mean*; 3.6 Doubly periodic functions*; 4 The Kepler problem; 4.1 The orbit of a planet lies on a plane which contains the Sun. |
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4.2 The line connecting the planet to the Sun sweeps equal areas in equal times4.3 Planets move along elliptical orbits with the Sun at a focus; 4.4 The ratio of the cube of the semi-major axis to the square of the period is the same for all planets; 4.5 The shape of the orbit; 5 The rigid body; 5.1 The moment of inertia; 5.2 Angular momentum; 5.3 Euler's equations; 5.4 Jacobi's solution; 6 Geometric theory of ordinary differential equations; 6.1 Phase space; 6.2 Differential manifolds; 6.3 Vector fields as derivations; 6.4 Fixed points; 7 Hamilton's principle; 7.1 Generalized momenta. |
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7.2 Poisson brackets7.3 The star product*; 7.4 Canonical transformation; 7.5 Infinitesimal canonical transformations; 7.6 Symmetries and conservation laws; 7.7 Generating function; 8 Geodesics; 8.1 The metric; 8.2 The variational principle; 8.3 The sphere; 8.4 Hyperbolic space; 8.5 Hamiltonian formulation of geodesics; 8.6 Geodesic formulation of Newtonian mechanics*; 8.7 Geodesics in general relativity*; 9 Hamilton-Jacobi theory; 9.1 Conjugate variables; 9.2 The Hamilton-Jacobi equation; 9.3 The Euler problem; 9.4 The classical limit of the Schrödinger equation* |
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9.5 Hamilton-Jacobi equation in Riemannian manifolds*9.6 Analogy to optics*; 10 Integrable systems; 10.1 The simple harmonic oscillator; 10.2 The general one-dimensional system; 10.3 Bohr-Sommerfeld quantization; 10.4 The Kepler problem; 10.5 The relativistic Kepler problem*; 10.6 Several degrees of freedom; 10.7 The heavy top; 11 The three body problem; 11.1 Preliminaries; 11.2 Scale invariance; 11.3 Jacobi co-ordinates; 11.4 The 1/r[Sup(2)] potential; 11.5 Montgomery's pair of pants; 12 The restricted three body problem; 12.1 The motion of the primaries; 12.2 The Lagrangian. |
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12.3 A useful identity12.4 Equilibrium points; 12.5 Hill's regions; 12.6 The second derivative of the potential; 12.7 Stability theory; 13 Magnetic fields; 13.1 The equations of motion; 13.2 Hamiltonian formalism; 13.3 Canonical momentum; 13.4 The Lagrangian; 13.5 The magnetic monopole*; 13.6 The Penning trap; 14 Poisson and symplectic manifolds; 14.1 Poisson brackets on the sphere; 14.2 Equations of motion; 14.3 Poisson manifolds; 14.4 Liouville's theorem; 15 Discrete time; 15.1 First order symplectic integrators; 15.2 Second order symplectic integrator; 15.3 Chaos with one degree of freedom. |
| Summary |
Classical Mechanics is the oldest and best understood part of physics. This does not mean that it is cast in marble yet, a museum piece to be admired from a distance. Instead, mechanics continues to be an active area of research by physicists and mathematicians. Every few years, we need to re-evaluate the purpose of learning mechanics and look at old material in the light of modern developments. Once you have learned basic mechanics (Newton's laws, the solution of the Kepler problem) and quantum mechanics (the Schrödinger equation, hydrogen atom) it is time to go back and relearn classical mech. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Mechanics -- Textbooks.
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Mechanics. |
| Genre/Form |
Textbooks.
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Electronic books.
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Textbooks.
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| Other Form: |
Print version: Rajeev, Sarada. Advanced mechanics : from Euler's determinism to Arnold's chaos. Oxford, United Kingdom : Oxford University Press, 2013 xiii, 163 pages 9780199670857 |
| ISBN |
9780191649875 (electronic book) |
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0191649872 (electronic book) |
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9780199670857 |
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