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Szydłowski, Marek; Heller, Michael; Sasin, Wiesław

Geometry of spaces with the Jacobi metric. (English) Zbl 0877.70010

J. Math. Phys. 37, No. 1, 346-360 (1996).
A generalized Maupertuis principle is formulated for systems whose Lagrangian has kinetic energy of indefinite sign. The metric for such systems, defined through kinetic energy, has a Lorenz signature. By using the geometric methods, the authors show that the trajectories of such systems are smooth, in the sense of the theory of differential spaces.
Reviewer: T.Atanackovic (Novi Sad)

Cited in 16 Documents

MSC:

70H30 Other variational principles in mechanics
83F05 Relativistic cosmology

Keywords:

kinetic energy of indefinite sign; smooth trajectories; generalized Maupertuis principle; Lagrangian; Lorenz signature; geometric methods; theory of differential spaces
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References:

[1] DOI: 10.1007/BF01291002 · Zbl 0030.22103 · doi:10.1007/BF01291002
[2] Kozlov V. V., Appl. Math. Mech. 40 pp 399– (1976)
[3] Kozlov V. V., Vestnik Mosk. Inst. Mat. Mech. (5) pp 118– (1977)
[4] Kozlov V. V., Usp. Mat. Nauk 40 pp 33– (1985)
[5] DOI: 10.1016/0960-0779(94)90151-1 · Zbl 0797.58079 · doi:10.1016/0960-0779(94)90151-1
[6] DOI: 10.1016/0960-0779(94)90151-1 · Zbl 0797.58079 · doi:10.1016/0960-0779(94)90151-1
[7] DOI: 10.1016/0960-0779(94)90151-1 · Zbl 0797.58079 · doi:10.1016/0960-0779(94)90151-1
[8] DOI: 10.1016/0960-0779(94)90151-1 · Zbl 0797.58079 · doi:10.1016/0960-0779(94)90151-1
[9] DOI: 10.1016/0960-0779(94)90151-1 · Zbl 0797.58079 · doi:10.1016/0960-0779(94)90151-1
[10] DOI: 10.1016/0960-0779(94)90151-1 · Zbl 0797.58079 · doi:10.1016/0960-0779(94)90151-1
[11] DOI: 10.1016/0960-0779(94)90151-1 · Zbl 0797.58079 · doi:10.1016/0960-0779(94)90151-1
[12] DOI: 10.1016/0960-0779(94)90151-1 · Zbl 0797.58079 · doi:10.1016/0960-0779(94)90151-1
[13] DOI: 10.1016/0960-0779(94)90151-1 · Zbl 0797.58079 · doi:10.1016/0960-0779(94)90151-1
[14] DOI: 10.1103/PhysRevD.47.5336 · doi:10.1103/PhysRevD.47.5336
[15] Sikorski S., Colloq. Math. 18 pp 251– (1967)
[16] Sikorski S., Colloq. Math. 24 pp 45– (1971)
[17] DOI: 10.1063/1.528098 · Zbl 0784.53045 · doi:10.1063/1.528098
[18] DOI: 10.1063/1.530575 · Zbl 0831.70010 · doi:10.1063/1.530575
[19] DOI: 10.1016/0001-8708(75)90139-5 · Zbl 0303.53032 · doi:10.1016/0001-8708(75)90139-5
[20] Tajmanov I. A., Usp. Mat. Nauk 47 pp 143– (1992)
[21] Bolotin S. W., Vestnik Mosk. Ins. Mat. Mech. (6) pp 72– (1978)
[22] DOI: 10.1088/0264-9381/10/9/022 · doi:10.1088/0264-9381/10/9/022
[23] DOI: 10.1007/BF01457066 · Zbl 0569.70017 · doi:10.1007/BF01457066
[24] DOI: 10.1007/BF01168606 · Zbl 0391.32004 · doi:10.1007/BF01168606
[25] DOI: 10.1016/0393-0440(92)90023-T · Zbl 0759.53010 · doi:10.1016/0393-0440(92)90023-T
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