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Mar 2013

Volume 54, Issue 3, Articles (03xxxx)

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J. Math. Phys. 54, 033512 (2013); http://dx.doi.org/10.1063/1.4794514 (20 pages)

Andrew Neate and Aubrey Truman
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back to top Classical Mechanics and Classical Fields

Rigid motions: Action-angles, relative cohomology and polynomials with roots on the unit circle

J.-P. Françoise, P. L. Garrido, and G. Gallavotti

J. Math. Phys. 54, 032901 (2013); http://dx.doi.org/10.1063/1.4794089 (19 pages)

Online Publication Date: 13 March 2013

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Revisiting canonical integration of the classical solid near a hyperbolic or elliptic uniform rotation, normal canonical coordinates p, q are constructed so that the Hamiltonian becomes a function (“normal form”) of x+ = pq or of x− = p2 + q2: the two cases are treated simultaneously distinguishing them, respectively, by a label a = ±, in terms of various power series with coefficients which are shown to be polynomials in a variable ra2 depending on the inertia moments. The normal forms are derived via the analysis of a relative cohomology problem and shown to be obtainable without reference to the construction of the normal coordinates via elliptic integrals (unlike the derivation of the normal coordinates p, q). Results and conjectures also emerge about the properties of the above polynomials and the location of their roots. In particular a class of polynomials with all roots on the unit circle arises.
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02.10.De Algebraic structures and number theory
02.30.-f Function theory, analysis

On the Hamilton-Jacobi theory for singular lagrangian systems

Manuel de León, Juan Carlos Marrero, David Martín de Diego, and Miguel Vaquero

J. Math. Phys. 54, 032902 (2013); http://dx.doi.org/10.1063/1.4796088 (32 pages)

Online Publication Date: 26 March 2013

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We develop a Hamilton-Jacobi theory for singular lagrangian systems using the Gotay-Nester-Hinds constraint algorithm. The procedure works even if the system has secondary constraints.
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45.05.+x General theory of classical mechanics of discrete systems
02.30.Jr Partial differential equations
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