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The rolling unrestrained brachistochrone

 

作者: Ju‐xing Yang,   David G. Stork,   David Galloway,  

 

期刊: American Journal of Physics  （AIP Available online 1987）
卷期: Volume 55, issue 9  

页码: 844-847

 

ISSN:0002-9505

 

年代: 1987

 

DOI:10.1119/1.15001

 

出版商: American Association of Physics Teachers

 

关键词: CLASSICAL MECHANICS;ROLLING;BOUNDARY−VALUE PROBLEMS;EQUATIONS OF MOTION;BENCH−SCALE EXPERIMENTS

 

数据来源: AIP

 

摘要:

We have generalized the unrestained brachistochrone problem to includerollingobjects in order to construct a demonstration brachistochrone track. Due to the nature of the constraints this well‐posed extremal problem cannot be solved using the techniques of Euler and Lagrange. The solution, parametrized by a measure of the generalized cylinder’s moment of inertia, reduces to that for the (sliding) unrestrained brachistochrone in the limit of vanishing moment of inertia.

 

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