2006
DOI: 10.1103/physrevlett.97.164302
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Global Invariants for Variable-Mass Systems

Abstract: We investigate the effect of mass loss on the invariants of single particle motion in potentials having translational or rotational symmetry. These systems are non-Hamiltonian in the physical momenta, but for non-velocity-dependent potentials can be made formally Hamiltonian by treating the velocities as canonical momenta. Applying Noether's theorem to the formal Hamiltonian then yields global invariants corresponding to its symmetries. For velocity-dependent potentials, an exact invariant is constructed from … Show more

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Cited by 3 publications
(6 citation statements)
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“…There are several other forces to consider, perhaps the most important being solar radiation pressure, which breaks the axisymmetry. The orbits of grains larger than about one micron are gravity dominated and are nearly unchanged by decreasing mass, although their total energy and angular momentum are proportional to m(t) [11]. Very small grains, with radii less than about 100 nm are magnetic dominated and strongly affected by changing q/m.…”
Section: Discussionmentioning
confidence: 97%
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“…There are several other forces to consider, perhaps the most important being solar radiation pressure, which breaks the axisymmetry. The orbits of grains larger than about one micron are gravity dominated and are nearly unchanged by decreasing mass, although their total energy and angular momentum are proportional to m(t) [11]. Very small grains, with radii less than about 100 nm are magnetic dominated and strongly affected by changing q/m.…”
Section: Discussionmentioning
confidence: 97%
“…In order to demonstrate the usefulness of the quasistatic effective potential, Fig. 7 shows three snapshots of an adiabatic orbit with v = 0.075 and χ 0 = 30 • , from t = 0-100, t = 400-500, and t = 900-1000, along with the corresponding energy boundaries found fromq and withp φ given by the adiabatic formula (11). The shrinking orbit is seen to closely follow the moving confinement boundary given by U e (ρ, z; t) = E, but does not reach ∂ E , owing to magnetic moment conservation.…”
Section: Example: Magnetic Dipolementioning
confidence: 99%
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