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| 库仑摩擦最速降曲线问题的讨论 |
| On Brachistochrone with Coulomb Friction |
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| DOI：10.3969/j.issn.1671-5322.2012.02.002 |
| 中文关键词: 变分法 变量变换不变性 最速降曲线 库仑摩擦 临界性 |
| 英文关键词: Calculus of variations variable transformation invariance Brachistochrone Coulomb friction Criticality |
| 基金项目: |
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| 摘要点击次数: 7962 |
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| 中文摘要: |
| 库仑摩擦轨道上的最速降线问题是一个受到众多研究者关注的问题。根据变分法及其变量变换不变性的性质，得到了轨道切线方向与菇轴的夹角及其对时间的导数构造可能极值函数能够满足的端点条件，以经典的无摩擦的最速降问题作了验证。据此，求得了库仑摩擦最速降线的解析表达式，分析归纳了库仑摩擦最速降轨迹斜率的匀变性、尺度的相似性、轨迹函数依摩擦系数的分簇性和运动的临界性等基本性质。 |
| 英文摘要: |
| Brachistochrone problem with Coulomb friction is a subject arising concerns of many researchers.Based on the variational method and the variable transformation invariance,we find the possible extremal function formed by slope angle of the tangent can meet the endpoint conditions and be verified by the classic brachistochrone problem.The analytical expression of the brachistochrone with Coulomb friction is obtained and the properties such as uniform trajectory slope,similar in scale,sub-cluster with the trajectory function of the friction coefficient and critical of the movement of brachistochrone with Coulomb friction are summarized. |
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