TY - JOUR

T1 - SO(4)-symmetry of mechanical systems with 3 degrees of freedom

AU - Bouarroudj, Sofiane

AU - Konstein, Semyon E.

PY - 2020/1/2

Y1 - 2020/1/2

N2 - We answered an old question: does there exist a mechanical system with 3 degrees of freedom, except for the Coulomb system, which has 6 first integrals generating the Lie algebra (Figure presented.) (4) by means of the Poisson brackets? A system which is not centrally symmetric, but has 6 first integrals generating Lie algebra (Figure presented.) (4), is presented. It is shown also that not every mechanical system with 3 degrees of freedom has first integrals generating (Figure presented.) (4).

AB - We answered an old question: does there exist a mechanical system with 3 degrees of freedom, except for the Coulomb system, which has 6 first integrals generating the Lie algebra (Figure presented.) (4) by means of the Poisson brackets? A system which is not centrally symmetric, but has 6 first integrals generating Lie algebra (Figure presented.) (4), is presented. It is shown also that not every mechanical system with 3 degrees of freedom has first integrals generating (Figure presented.) (4).

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U2 - 10.1080/14029251.2020.1683997

DO - 10.1080/14029251.2020.1683997

M3 - Article

AN - SCOPUS:85074142795

VL - 27

SP - 162

EP - 169

JO - Journal of Nonlinear Mathematical Physics

JF - Journal of Nonlinear Mathematical Physics

SN - 1402-9251

IS - 1

ER -