Introduction to mechanics and symmetry

By Jerrold E. Marsden, Tudor S. Ratiu. 1994

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Citations in the corpus

Feedback Systems: An Introduction for Scientists and Engineers (2008, unknown): “For students with a strong interest in mechanics, the text by Marsden and Ratiu [MR94] provides a very elegant approach using tools from differential geometry.”
Momentum maps and measure-valued solutions (peakons, filaments, and sheets) for the EPDiff equation (2003, methodology): “(See Marsden and Ratiu [1999] for a discussion.”
The geometric structure of unit dual quaternion with application in kinematic control (2012, background): “It is well known that Qu is diffeomorphic to manifold S3 [21], thus we conclude that Qu is a manifold with three dimensions.”
Analytic solutions and triality theory for nonconvex and nonsmooth variational problems with applications (2000, background): “In geometrically linear convex systems, the symmetry between the primal and dual systems are amazingly beautiful (see, [42,54]).”
Global well–posedness for the Lagrangian averaged Navier–Stokes (LANS–α) equations on bounded domains (2001, methodology): “The reduction of the equations from material to spatial (Eulerian) representation may be viewed by the now classical technique of Euler{Poincaré reduction which we brie®y review below; see Marsden & Ratiu (1999) and Holm et al. (1998b) for an exposition and further references.”
Controlled symmetries and passive walking (2005, background): “For more details we refer the reader to [17], [18].”
Structure-preserving discretization of incompressible fluids (2009, unknown): “and (see [6]) i[u,w]v = Luiwv − iwLuv, we have ∫”
Some Geometric Evolution Equations Arising as Geodesic Equations on Groups of Diffeomorphisms Including the Hamiltonian Approach (2006, methodology): “This is, of course, just the Euler-Poincaré equation for right invariant systems using the Lagrangian given by the kinetic energy (see [34], section 13).”
A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank (2013, background): “Remark 4 Geodesics on Lie groups for the right-invariant metric are widespread in Lagrangian and symplectic dynamics; see, e.g., Marsden & Tudor (1999).”
Robust hybrid control for autonomous vehicle motion planning (2000, unknown): “A simple de nition that is enough for the purpose of this paper is given in the following: for further details and a precise de nition in a Hamiltonian mechanics framework, see [10, 11].”