The problem of three bodies which attract each other with forces proportional to the cube of the inverse of their distance and move on a line was reduced to one quadrature by Jacobi [23]. Here we show that the equations of motions admit a five-dimensional Lie symmetry algebra and can be reduced to a single second-order linear equation, i.e. the equation of motion of a single free particle on the line.
NUCCI, M.C. (2005). Jacobi's three-body system moves like a free particle. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 12-suppl. 1, 499-506 [10.2991/jnmp.2005.12.s1.40].
Jacobi's three-body system moves like a free particle
NUCCI, Maria Clara
2005
Abstract
The problem of three bodies which attract each other with forces proportional to the cube of the inverse of their distance and move on a line was reduced to one quadrature by Jacobi [23]. Here we show that the equations of motions admit a five-dimensional Lie symmetry algebra and can be reduced to a single second-order linear equation, i.e. the equation of motion of a single free particle on the line.File in questo prodotto:
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