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.
Jacobi's three-body system moves like a free particle
NUCCI, Maria Clara
2005-01-01
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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