Generalized Gantmacher formulas through functions of matrices
作者:
Leon Y. Bahar,
期刊:
American Journal of Physics
(AIP Available online 1991)
卷期:
Volume 59,
issue 12
页码: 1103-1111
ISSN:0002-9505
年代: 1991
DOI:10.1119/1.16621
出版商: American Association of Physics Teachers
关键词: EQUATIONS OF MOTION;ANGULAR ACCELERATION;CORIOLIS FORCE;MATRICES;CLASSICAL MECHANICS;ROTATION
数据来源: AIP
摘要:
Gantmacher formulas are generalized by including the effect of the centripetal and angular accelerations in addition to the usual Coriolis term. The integration is accomplished by using a method based on functions of matrices, which permits the summation of an infinite series in closed form through the use of the Cayley–Hamilton theorem. The problem is further extended by allowing arbitrary matrix coefficients in the vector equation of motion, provided they obey a certain commutativity condition. In addition to standard examples, the problem of a particle moving on a plane rotating with variable angular velocity is considered. This example differs from the ones considered in the literature because neither the centripetal nor the angular acceleration terms can be neglected. Solutions of various orders are developed by truncating the exact solution when appropriate.
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