Chapter

Lagrangian and Hamiltonian mechanics

D. Violeau

in Fluid Mechanics and the SPH Method

Published in print May 2012 | ISBN: 9780199655526
Published online September 2012 | e-ISBN: 9780191741227 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199655526.003.0001
Lagrangian and Hamiltonian mechanics

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This chapter details the basics of Lagrangian and Hamiltonian mechanics. From the basic principles of mechanics (Galilean invariance, least action principle), the chapter builds the fundamental equations of motion of a set of points named ‘particles’ (Lagrange and Hamilton equations), and introduces the conservation laws in connection with the symmetry of space–time. It also brings in the concept of internal energy for systems composed of several individual beings, and make the distinction between internal and external forces. Rigid body motion is rapidly treated for the needs of Chapters 5 and 6. Lastly, the concept of pressure is introduced.

Keywords: Lagrangian; Lagrange equations; Hamilton equations; conservation laws; least action principle

Chapter.  26650 words.  Illustrated.

Subjects: Condensed Matter Physics

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