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Nonuniqueness in the solutions of Newton’s equation of motion

 

作者: Abhishek Dhar,  

 

期刊: American Journal of Physics  （AIP Available online 1993）
卷期: Volume 61, issue 1  

页码: 58-61

 

ISSN:0002-9505

 

年代: 1993

 

DOI:10.1119/1.17411

 

出版商: American Association of Physics Teachers

 

关键词: EQUATIONS OF MOTION;SINGULARITY;INITIAL CONDITIONS;FORCES;CLASSICAL MECHANICS;DIFFERENTIAL EQUATIONS

 

数据来源: AIP

 

摘要:

In the case of singular forces, for which some of the higher derivatives do not exist at a given point, it is not generally true that Newton’s equations of motion will give unique solutions for given initial conditions. In this paper, the motion of a particle in a one‐dimensional conservative force field is considered. The necessary and sufficient conditions that ensure unique solutions are determined.

 

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