Solved Problems in Lagrangian and Hamiltonian MechanicsThe aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general. |
Contents
| 1 | |
| 9 | |
Problem Solutions | 24 |
Lagrangian Systems | 51 |
Problem Statements | 57 |
Problem Solutions | 76 |
Hamiltons Principle | 111 |
Problem Statements | 116 |
Problem Solutions | 252 |
Integrable Systems | 281 |
Problem Statements | 289 |
Problem Solutions | 305 |
QuasiIntegrable Systems | 341 |
Problem Statements | 347 |
Problem Solutions | 358 |
From Order to Chaos | 385 |
Problem Solutions | 131 |
Hamiltonian Formalism | 165 |
Problem Statements | 171 |
HamiltonJacobi Formalism 233 | 232 |
Problem Statements | 239 |
Problem Statements | 396 |
Problem Solutions | 415 |
| 456 | |
Other editions - View all
Solved Problems in Lagrangian and Hamiltonian Mechanics Claude Gignoux,Bernard Silvestre-Brac No preview available - 2009 |
Solved Problems in Lagrangian and Hamiltonian Mechanics Claude Gignoux,Bernard Silvestre-Brac No preview available - 2009 |
Solved Problems in Lagrangian and Hamiltonian Mechanics Claude Gignoux,Bernard Silvestre-Brac No preview available - 2014 |
Common terms and phrases
acceleration action allows angle angular frequency assume axis calculate canonical choose close concerning condition Consequently consider const constant constraint coordinates corresponding curve Deduce defined depends derivative determined differential equation direction distance equal exists expression field Figure Finally fixed point force frame function Give given Hamilton Hamiltonian harmonic implies initial integral introduce invariant kinetic energy known Lagrange equation Lagrangian leads linear magnetic mapping mass momentum motion moving obtained orbit origin particle particular pendulum perform period perturbation phase space plane position potential principle problem provides quantity question radius reduced relation remains respect result rotation Show simple solution solve speed stability Statement surface trajectory transformation variable variation vector velocity vertical wall wave write written