Journal article
Generalized Gantmacher formulas through functions of matrices
American journal of physics, v 59(12), pp 1103-1111
Dec 1991
Abstract
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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Details
- Title
- Generalized Gantmacher formulas through functions of matrices
- Creators
- Leon Y. Bahar - Drexel University
- Publication Details
- American journal of physics, v 59(12), pp 1103-1111
- Number of pages
- 9
- Resource Type
- Journal article
- Academic Unit
- [Retired Faculty]
- Web of Science ID
- WOS:A1991GQ78300011
- Other Identifier
- 991019184079204721
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- Web of Science research areas
- Education, Scientific Disciplines
- Physics, Multidisciplinary