Families of planar orbits generated by homogeneous potentials |
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| Authors: | George Bozis Simela Grigoriadou |
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| Institution: | (1) Department of Theoretical Mechanics, University of Thessaloniki, GR-540 06 Thessaloniki, Greece |
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| Abstract: | The second order partial differential equation which relates the potentialV(x,y) to a family of planar orbitsf(x,y)=c generated by this potential is applied for the case of homogeneousV(x,y) of any degreem. It is shown that, if the functionf(x,y) is also homogeneous, there exists, for eachm, a monoparametric set of homogeneous potentials which are the solutions of an ordinary, linear differential equation of the second order. Iff(x,y) is not homogeneous, in general, there is not a homogeneous potential which can create the given family; only if  =f
y
/f
x
satisfies two conditions, a homogeneous potential does exist and can be determined uniquely, apart from a multiplicative constant. Examples are offered for all cases. |
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| Keywords: | Inverse problem homogeneous potential |
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