Abraham, R., & Marsden, J. (1978). Foundations of Mechanics. The BenjaminCummings Publishing Company, Inc., London. Home/Search Document Not in Database Summary Related Articles Check |
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The Dynamics of Parallel Transport - Patrick (2000) (Correct)
....geodesics can be scrutinized by experimenting with the paths of free particles. This brings dynamical concepts to Riemannian geometry, and a recent text in the subject ( 3] also presents classical mechanics, even though its author s aims seem purely geometric. Indeed, as Abraham and Marsden ([1], page 225) mention, one can start with the Hamiltonian approach as basic and de ne the covariant derivative, and so forth, in terms of this structure. Some aspects of Riemannian geometry are often explained from the point of view what residents of the manifold would naturally ....
....moving relativistically in spacetime, but are spinning non relativistically. Exactly as above use the exponential map to embed the lament into spacetime. The lament will have total rest mass m 0 and rest length 2 . The relativistic replacement for the nonrelativistic kinetic energy (1) is (see [1] or [5] T = m 0 c dx: In coordinates, 7) is the expansion of g V (x) V (x) in x to order 2. Using Equations (9) and (10) to simplify the coecient of x , and exchanging the derivative of g ij for a Christo el symbols in the coecient of x, gives ....
Abraham, R.; Marsden, J. E.: Foundations of Mechanics. Addision-Wesley, second edition, 1978.
Infinite Dimensional Hamiltonian Systems with Symmetries - Schmid (Correct)
....(integral curves) of the vector field XH i.e. F = XH (F ) H , dt . 2.1) 3 Examples of Poisson manifolds and Hamilton s equations 3. 1 Finite dimensional classical mechanics There are many well known texts on the geometric treatment of classical mechanics, e.g. Abraham and Marsden [1], Arnold [8] Choquet Bruhat, DeWitt Morette and Dillard Bleick [17] Goldstein [25] Guillemin and Sternberg [26] Marle and Libermann [38] Marmo, Saletan, Simoni and Vitali [39] Marsden and Ratiu [43] Marsden [41] Souriau [61] For finite dimensional classical mechanics we take P = IR ....
Abraham, R., Marsden, J.E. Foundations of Mechanics, 2nd ed., Addison-Wesley, Reading Mass. 1978.
A Universal Reduction Procedure for Hamiltonian Group Actions - Arms, Cushman, Gotay (1991) (3 citations) (Correct)
....we explicitly construct the reduced spaces and their Poisson algebras for the spherical pendulum. 1 Introduction Reduction of the order of mechanical systems with symmetry is a venerable topic dating back to Jacobi, Routh and Poincare. Although reduction in the regular case is well understood [1, 2], interesting and important applications continue to arise [3, 4] See also [5] for a comprehensive exposition. The singular case has received much less attention, despite the growing realization that it is the rule rather than the exception. See for instance [6 11] For example, the solution ....
....For example, let M = T # G with G acting on M by the lift of left translation. Let J : M # be the momentum map given by J(# g ) R # g # g for # g M . Every is a regular value of J and M = J 1 ( G is symplectically di#eomorphic to with its KostantKirillov symplectic structure [1]. On the other hand, T # G G is isomorphic as a Poisson manifold to # with its Lie Poisson structure [4] Thus the basic 5 commutative diagram (1) becomes J 1 ( ## T # G ##G # where i is the inclusion mapping. Now suppose that is not closed in # . Then the Marsden Weinstein ....
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Abraham, R. and Marsden, J., Foundations of Mechanics,2 edition, Benjamin/Cummings, Reading, 1978.
Are Hamiltonian Flows Geodesic Flows? - Mccord, Meyer, Offin (2002) (Correct)
....bundle or the cotangent bundle T M . The cotangent bundle has a natural symplectic structure and so the function G considered as a Hamiltonian defines a Hamiltonian flow on T M . This flow is the same as the geodesic flow defined by the metric G when it is transfered to the cotangent bundle [1]. In this paper we begin the study of the inverse problem [10] and ask when is a Hamiltonian flow a geodesic flow, or more generally a reparameterization of a geodesic flow. There are important classical results along these lines. ffl A collection of holonomic constraints on a mechanical system ....
....as a Riemannian metric on M , and H as a Hamiltonian on the symplectic manifold T M . The Jacobi metric is G = h Gamma V ) K, with h a constant. It is a well defined metric at those points of M where V h. The geodesic flow on G = 1 is a reparameterization of the Hamiltonian flow on H = h [1, 30]. The flow of the spherical pendulum on an energy level sufficiently high that the bob can go Date: October 25, 2002. 1991 Mathematics Subject Classification. 34C35, 34C27, 54H20. Key words and phrases. Hamiltonian systems, geodesic flows, Jacobi metric, three body problem. This research ....
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R. Abraham and J. Marsden, Foundations of Mechanics, Benjamin Cummings, London, 1978.
Obstruction Results in Quantization Theory - Gotay, Grundling (1996) (1 citation) (Correct)
....representation # # on a domain D # that does. In such cases we will suppose that the representation has been so extended. 4 Examples In this section we present the gist of the arguments that there are no nontrivial quantizations of either or . The complete proofs can be found in [AM, Ch1, Fo , Go1, Gr, GS, VH1, VH2] for R and in [GGH] for S . In both cases the detailed structure of the Poisson algebras and their representation theory is used, which makes it hard to generalize these results to other symplectic manifolds. Finally, we show following [Go3] that there is a full quantization of for each ....
Abraham, R. & Marsden, J.E. [1978] Foundations of Mechanics. Second Ed. (Benjamin-Cummings, Reading, MA).
Visual Servo with Dynamics: Control of an Unmanned Blimp - Hong Zhang James (Correct)
....g; g g) for = g g. These equations can be written as Gamma ad = C( u ; 7) where denotes the external forces written as body forces, and ad represents the dual of the adjoint action and is a constant linear map dependent only on the particular choice of Lie group, G (see [16, 1] for more details) Here, input forces are written separately for more visibility. We remark that this type of reduction can also be performed for most robotic locomotion systems, including wheeled mobile robots and satellites with robotic arms [19] Whether taken directly from Eq. 7, or more ....
R. Abraham and J. E. Marsden. Foundations of Mechanics. Addison-Wesley, Reading, MA, second edition, 1978.
Motion Control Algorithms for Simple Mechanical Systems.. - Martínez, al. (Correct)
....on Q and 2(Q) the set of smooth vector fields on Q. Throughout the paper, the manifold Q and the mathematical objects defined on it will be assumed analytic. Associated with the Riemannian metric 6 there is a natural ane connection, called the Levi Civita connection. An ajfine connection [1, 23] is defined as an assignment v: 2(0) x 2(0) 2(0) x,r) Vxr which is ] bilinear and satisfies VfxY fVxY and Vx(fY) fVxY X(f)Y, for any X, Y C 2(Q) f C(Q) This implies that VxY(q) only depends on X(q) and the value of Y along a curve which is tangent to X at q. Let c: t [a,b] c(t) ....
.... X3( X1, X2) X2, X3, X1] X1, X2, X3] 6(X3, X1, X2] where Xi (Q) The Christoffel symbols of V are Fbac 6ad ( O6db 06tic 06bc ) where (6 ad) denotes the inverse of the matrix (6d 6(O Oq , O Oq) The geodesics of V 6 are precisely the solutions of the classical EulerLagrange equations [1] for the kinetic energy Lagrangian, L . Instead of the input forces F, F , we shall make use of the input accelerations Y, Y, defined as (Y , If Y Y,f(q) the control equations read Oq , tbq q ui(t)Y,f(q) 1 a n. 1) or, in vector field notation, t) Z(x) ....
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Abraham, R. and 3. E. Marsden: 1978, Foundations of Mechanics. Reading, MA: Benjamin-Cummings, 2nd edition.
Linear Hamiltonian systems - Rapisarda, Trentelman (Correct)
....external variables can qualify for Hamiltonianity. This point of view is in contrast with the usual definition of autonomous Hamiltonian system, in which a symplectic structure on the space of the external variables (and consequently, an even number of such variables) is assumed (see for example [1], 2] The authors believe that in order to investigate linear, finite dimensional Hamiltonian systems, Definition 2.1 is a more natural starting point than the classical one. In order to support our claim, we consider the following example. Example 2.1. Consider a spring mass system without ....
Abraham, R. and Marsden, J.E., Foundations of mechanics, Benjamin/Cummings, NY, 1978.
Reconstruction Phases for Hamiltonian Systems on Cotangent Bundles - Blaom (Correct)
....Theorem 2.3. 2.1. An abstract setting for reconstruction phases. Assume G is a connected Lie group acting symplectically from the left on a smooth (C # ) symplectic manifold (P, #) and assume the existence of an Ad # equivariant momentum map J : P g # . For relevant background, see [14, 1, 18]. Here g denotes the Lie algebra of G. Assume G acts freely and properly, and that the fibers of J are connected. All these hypotheses hold in the case P =T # Q when we take G to act by cotangent lifting a free and proper action on Q and assume Q is connected; details will be recalled in Section ....
R. Abraham and J. E. Marsden. Foundations of Mechanics. Addison-Wesley Publishing Co., Reading, Massachusetts, 2nd edition, 1978.
Symplectic Nonlinear Component - Analysis Lucas Parra (Correct)
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Abraham, R., & Marsden, J. (1978). Foundations of Mechanics. The BenjaminCummings Publishing Company, Inc., London.
Redundancy Reduction with Information - Preserving Nonlinear Maps (Correct)
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Abraham, R., & Marsden, J. (1978). Foundations of Mechanics. The BenjaminCummings Publishing Company, Inc., London.
Submitted to AUTOMATICA, July 20th, 1999 - The Geometry Of (Correct)
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R. Abraham and J. E. Marsden. Foundations of mechanics. Addison-Wesley, 2nd edition, 1978.
An Ergodic Arnold{Liouville - Theorem For Locally (Correct)
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Abraham, R., and J.E. Marsden, Foundations of Mechanics. Second Edition, Addison Wesley, Redwood City, 1987
Set Oriented Numerical Methods in Space Mission Design - Dellnitz, Junge (2005) (Correct)
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R. Abraham and J.E. Marsden. Foundations of Mechanics. Second Edition, Addison-Wesley, 1978.
Elliptic Integrable Systems of Calogero-Moser Type: A Survey - Ruijsenaars (Correct)
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R. Abraham and J. E. Marsden, Foundations of mechanics, 2nd ed., Benjamin-Cummings, 1978.
Riemannian Observers for Euler-Lagrange Systems - Anisi, Hamberg (Correct)
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Abraham, R. and J.E. Marsden (1978). Foundations of Mechanics. Addison-Wesley.
Nonlinear Control of Underactuated Mechanical Systems with.. - Olfati-Saber (2001) (Correct)
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R. Abraham and J. E. Marsden. Foundations of Mechanics. Addison-Wesley, 1978.
The Inverse Problem for Euler's Equation on Two and Three.. - Lawton (2002) (Correct)
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R Abraham and JE Marsden (1978) Foundations of Mechanics, Benjamin, London.
A Priori Estimates for the Global Error Committed by Runge-Kutta.. - Niesen (2001) (Correct)
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R. Abraham and J. E. Marsden. Foundations of Mechanics. Benjamin /Cummings, Reading, MA, second edition, 1978.
A Groenevold-Van Hove Theorem for S² - Gotay, Grundling, Hurst (1996) (Correct)
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Abraham, R. and Marsden, J.E. [1978] Foundations of Mechanics. Second ed. (Benjamin-Cummings, Reading, MA). MR 81e:58025
Homoclinic Billiard Orbits Inside Symmetrically - Perturbed Ellipsoids Amadeu (Correct)
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R. Abraham and J.E. Marsden. Foundations of mechanics. Benjamin/Cummings Pub. Co., Reading, Mass., 1978.
Two Axially Symmetric Coupled Rigid Bodies: Relative Equilibria.. - Patrick (1991) (1 citation) (Correct)
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R. Abraham & J. E. Marsden, Foundations of Mechanics, Second Edition, AddisonWesley, Reading, Mass., 1978.
Article Submitted to ***Journal title*** - Stability Of Rotating (Correct)
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R. Abraham, J. Marsden, Foundations of Mechanics, 2nd rev. Edition, Perseus Press, (1994).
Dual Mixed Volumes and Isosystolic Inequalities - Paiva (Correct)
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R. Abraham and J.E. Marsden, "Foundations of mechanics" 2nd ed, The Benjamin /Cummings Publishing Company Inc., Reading, Massachusetts, 1978.
Asymptotic Properties of the Differential Equation.. - Asch, Benguria, Stovicek (Correct)
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Abraham R., Marsden J.E.: Foundations of Mechanics. Addison-Wesley, 1978.
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