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- W1975845082 abstract "Consider Lagrange's integrable case of the motion of a rigid body about a fixed point, when the center of gravity of the body lies on the polar axis of the spheroid of inertia of the body [l, case II, pp. 216— 249]. In [l, §110, pp. 233-235] one finds An interesting proof that the precession for a complete period has the same sign as uk (which) has been given by Hadamard (see [2]). Hadamard's proof employs the theory of residues of functions of a complex variable. Quite recently (see [3], which cites the recent literature), upper and lower bounds for the apsidal angle in the theory of the heavy symmetrical top have been obtained by an elementary method, not relying upon the theory of residues. This same direct method applies equally well in deducing Hadamard's result. This application will be carried out here, in the notation of [l], for the immediate comparison of the two methods. The argument requires the preliminary evaluation of two simple definite integrals:" @default.
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- W1975845082 date "1962-04-01" @default.
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- W1975845082 title "On a result of Hadamard concerning the sign of the precession of a heavy symmetrical top" @default.
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- W1975845082 doi "https://doi.org/10.1090/s0002-9939-1962-0139287-8" @default.
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