Jacobi fields in nonholonomic mechanics
AA Simoes, JC Marrero… - Journal of Physics A …, 2022 - iopscience.iop.org
Journal of Physics A: Mathematical and Theoretical, 2022•iopscience.iop.org
In this paper, we define Jacobi fields for nonholonomic mechanics using a similar
characterization than in Riemannian geometry. We give explicit conditions to find Jacobi
fields and finally we find the nonholonomic Jacobi fields in two equivalent ways: the first one,
using an appropriate complete lift of the nonholonomic system and, in the second one, using
the curvature and torsion of the associated nonholonomic connection.
characterization than in Riemannian geometry. We give explicit conditions to find Jacobi
fields and finally we find the nonholonomic Jacobi fields in two equivalent ways: the first one,
using an appropriate complete lift of the nonholonomic system and, in the second one, using
the curvature and torsion of the associated nonholonomic connection.
Abstract
In this paper, we define Jacobi fields for nonholonomic mechanics using a similar characterization than in Riemannian geometry. We give explicit conditions to find Jacobi fields and finally we find the nonholonomic Jacobi fields in two equivalent ways: the first one, using an appropriate complete lift of the nonholonomic system and, in the second one, using the curvature and torsion of the associated nonholonomic connection.
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