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Hamiltonian formalism for particles with a generalized rigidity. (English. Russian original) Zbl 1086.37523
Theor. Math. Phys. 117, No. 1, 1214-1222 (1998); translation from Teor. Mat. Fiz. 117, No. 1, 130-139 (1998).
Summary: We develop a Hamiltonian formalism for mechanical systems with reparametrization-invariant Lagrangians dependent on the extrinsic curvature of a world line. We construct complete sets of constraints for Lagrangians with quadratic dependence on the extrinsic curvatures, for Lagrangians proportional to an arbitrary extrinsic curvature, and for Lagrangians linearly dependent on the first two curvatures.

37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
70H05 Hamilton’s equations
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
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[1] M. M. Postnikov,Smooth Manifolds. Lectures in Geometry. Semester III. [in Russian], Vol. 1, Nauka, Moscow (1987); English transl., URSS, Moscow (1994).
[2] A. M. Polyakov,Nucl. Phys. B,268, 406 (1986);Mod. Phys. Lett. A,3, 112 (1988).
[3] M. S. Plyushchay,Nucl. Phys. B,362, 54 (1991); Yu. A. Kuznetsov and M. S. Plyushchay,Nucl. Phys. B,389, 181 (1993).
[4] M. S. Plyushchay,Phys. Lett. B.,243, 383 (1990). · Zbl 1332.81110
[5] M. S. Plyushchay,Phys. Lett. B.,253, 50 (1991).
[6] A. A. Kapustnikov, A. Pashnev and A. Pichugin,Phys. Rev. D.,55, 2257 (1997).
[7] E. Ramos and J. Roca,Nucl. Phys. B,436, 529 (1995). · Zbl 1052.81614
[8] E. Ramos and J. Roca,Nucl. Phys. B.,452, 705 (1995). · Zbl 0925.53043
[9] I. V. Tyutin, Private communication (1998).
[10] E. Ramos and J. Roca,Nucl. Phys. B,477, 606 (1996). · Zbl 0925.81046
[11] V. D. Gershun and A. I. Pashnev,Theor. Math. Phys.,73, 1227 (1987).
[12] A. P. Isaev, and A. T. Filippov,Mod. Phys. Lett. A,4, 2167, (1989).
[13] A. Pashnev and M. Tsulaya, ”Description of the higher massless irreducible integer spins in the BRST approach”, hep-th/9803207; Preprint E2-98-56, JINR, Dubna (1998).
[14] A. Pashnev and M. Tsulaya, In preparation.
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