On rotationally invariant integrable and superintegrable classical systems in magnetic fields with nonsubgroup type integrals
Abstract
The aim of the present article is to construct quadratically integrable three dimensional systems in nonvanishing magnetic fields which possess socalled nonsubgroup type integrals. The presence of such integrals means that the system possesses a pair of integrals of motion in involution which are (at most) quadratic in momenta and whose leading order terms, that are necessarily elements of the enveloping algebra of the Euclidean algebra, are not quadratic Casimir operators of a chain of its subalgebras. By imposing in addition that one of the integrals has the leading order term [ image ] we can consider three such commuting pairs: circular parabolic, oblate spheroidal and prolate spheroidal. We find all possible integrable systems possessing such structure of commuting integrals and describe their Hamiltonians and their integrals.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 May 2019
 DOI:
 10.1088/17518121/ab14c2
 arXiv:
 arXiv:1812.09399
 Bibcode:
 2019JPhA...52s5201B
 Keywords:

 integrability;
 superintegrability;
 classical mechanics;
 magnetic field;
 Mathematical Physics;
 37J35;
 78A25
 EPrint:
 doi:10.1088/17518121/ab14c2