An exact solution for a particle in a velocity-dependent force field
作者:
Julio M. Yáñez,
Gonzalo Gutiérrez,
Felipe González-Cataldo,
David Laroze,
期刊:
American Journal of Physics
(AIP Available online 2021)
卷期:
Volume 89,
issue 12
页码: 1103-1112
ISSN:0002-9505
年代: 2021
DOI:10.1119/10.0005992
出版商: American Association of Physics Teachers
数据来源: AIP
摘要:
We revisit the classical mechanics problem of a particle moving under the influence of a force that depends on its velocity. Using the properties of the rotation matrix and associated operators, we show that it is possible to find an exact analytical solution to a number of problems where the differential equation of motion depends on the velocity. First, we apply our method to the well-known cases of a particle under the influence of the Lorentz force and Coriolis force, providing the complete analytical solution in each case for the motion of the particle in three dimensions. We also show that the complete solution can be obtained when the centrifugal force is included, showing the applicability to cases where there is simultaneous dependence on the position and velocity. This method, which is not currently discussed in a typical course in elementary mechanics, provides an alternative approach to the traditional methods that are used to solve these types of problems.
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