Study on Hamel’s Embedding Method via the Udwadia-Kalaba Theory

ZHAO Han; ZHAO Xiao-min; JIANG Jian-man

doi:10.21656/1000-0887.370327

Volume 38 Issue 6

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ZHAO Han, ZHAO Xiao-min, JIANG Jian-man. Study on Hamel’s Embedding Method via the Udwadia-Kalaba Theory[J]. Applied Mathematics and Mechanics, 2017, 38(6): 696-707. doi: 10.21656/1000-0887.370327

Citation:

ZHAO Han, ZHAO Xiao-min, JIANG Jian-man. Study on Hamel’s Embedding Method via the Udwadia-Kalaba Theory[J]. Applied Mathematics and Mechanics, 2017, 38(6): 696-707. doi: 10.21656/1000-0887.370327

Citation:

ZHAO Han, ZHAO Xiao-min, JIANG Jian-man. Study on Hamel’s Embedding Method via the Udwadia-Kalaba Theory[J]. Applied Mathematics and Mechanics, 2017, 38(6): 696-707. doi: 10.21656/1000-0887.370327

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Study on Hamel’s Embedding Method via the Udwadia-Kalaba Theory

doi: 10.21656/1000-0887.370327

¹School of Mechanical Engineering, Hefei University of Technology, Hefei 230009, P.R.China;²School of Automotive and Traffic Engineering, Hefei University of Technology, Hefei 230009, P.R.China

Received Date: 2016-10-24
Rev Recd Date: 2016-11-21
Publish Date: 2017-06-15

Abstract

Abstract

Hamel embedded the constraint directly into the kinetic energy of unconstrained motion to avoid the use of Lagrange multiplier, which made a simple, straightforward, but incompletely correct method. Hamel stated that this method may lead to wrong results, but did not point out the applicable conditions for its correctness. Based on the Udwadia-Kalaba theory, the necessary and sufficient condition for Hamel’s embedding method was found. Besides, examples show that Rosenberg’s work on the validity of Hamel’s embedding method is insufficient. Hamel’s embedding method may be correct under nonholonomic constraint and may be incorrect under holonomic constraint. According to the theoretical and exemplary analysis, the correctness of Hamel’s embedding method is not only determined by the constraints, but also determined by the mechanical system model.
- Hamel’s embedding method,
- Udwadia-Kalaba theory,
- holonomic constraint,
- nonholonomic constraint,
- mechanical system model

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References(15)

References

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