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Imperial College London
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by DD Holm - 2011 - Cited by 91 - Related articles
Sep 24, 2011 - WSPC/Book Trim Size for 9in by 6in. Contents. Preface xv. 1 Galileo. 1. 1.1 Principle of Galilean ... 2.3.2 Infinitesimal transformations of a Lie group. 40 ..... inside a uniformly moving ship would be unable to determine by mea-.[PDF]Geometric Mechanics, Part II: Rotating, Translating and ...
www2.imperial.ac.uk/~dholm/.../GeomMech2.p...
Imperial College London
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by DD Holm - Cited by 92 - Related articles
1 Galileo. 1. 1.1 Principle of Galilean relativity . . . . . . . . . . . . . . 1. 1.2 Galilean transformations . . . . . . . . . . . . . . . . . ... 2.3.2 Infinitesimal transformations of a Lie group . . 31 ..... ship are unable to determine by measurements made inside it whether.The Darwin force is usually small; so it is often neglected.
Only the Coriolis force depends on the velocity in the moving
frame. The Coriolis force is very important in largescale
motions on Earth. For example, pressure balance with
the Coriolis force dominates the (geostrophic) motion of
weather systems that comprise the climate.
The centrifugal force is important, for example, in obtaining
orbital equilibria in gravitationally attracting systems.
Lie symmetries and conservation laws
Emmy Noether
Recall from Definition 1.2.3 that a Lie
group depends smoothly on its parameters.
(See Appendix B for more details.)
Definition 2.3.1 (Lie symmetry) Asmooth
transformation of variables ft; qg depending
on a single parameter s defined by
ft; qg 7! f t(t; q; s); q(t; q; s)g ;
that leaves the action S =
R
Ldt invariant
is called a Lie symmetry of the action.
Theorem 2.3.1 (Noether’s theorem) Each Lie symmetry of the action
for a Lagrangian system defined on a manifold M
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