## Abstract

Finite (polynomial) solutions of Laplace's equation are investigated. The unifying features of this study are the so-called Niven equations which yield the dimension of the space of such solutions. In carrying out this study complete sets of solutions are obtained on the n-dimensional sphere in terms of ellipsoidal coordinates. This corresponds to an integrable system having all the integrals of motion given by quadratic orbits of the universal enveloping algebra of O(n+1). They call this system the n-dimensional Euler top. The spectrum of the integrals of motion has been recently computed for n=3 by Komarov and Kuznetsov (1991) using results originally due to Niven (1891). These calculations are extended to arbitrary dimension.

Original language | English (US) |
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Article number | 022 |

Pages (from-to) | 5663-5675 |

Number of pages | 13 |

Journal | Journal of Physics A: General Physics |

Volume | 25 |

Issue number | 21 |

DOIs | |

State | Published - 1992 |

Externally published | Yes |