| 具有黏滞阻力时的最速降线 |
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| 引用本文： | 周嘉炜, 曹炳阳, 过增元. 具有黏滞阻力时的最速降线[J]. 力学与实践, 2011, 33(3): 11-14. doi: 10.6052/1000-0879-lxysj2011-123 |
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| 作者姓名： | 周嘉炜 曹炳阳 过增元 |
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| 作者单位： | 1. 清华大学 工程力学系; 2. 清华大学工程力学系 |
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| 基金项目： | 清华大学自主科研计划资助项目 |
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| 摘 要： | 针对实际应用中存在黏滞阻力的最速降线的问题, 首先推导出适于此类问题的解除约束的广义变分原理, 它适用于具有摩擦阻尼和多自由度系统优化的问题. 得到描述有黏滞阻力情况下最速降线相关函数的微分方程, 它在黏滞阻力为零时即退化为滚轮线. 利用MATLAB数值计算给出了最速降线受黏滞阻力的影响: 在黏滞阻力系数较小时最速降线趋于变凹, 当阻力系数增大到一定值之后最速降线趋于平缓, 当阻力系数很大时最速降线趋于直线.
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| 关 键 词： | 最速降线 粘滞阻力 广义变分原理 拉格郎日乘子法 |
| 收稿时间： | 2011-03-28 |
| 修稿时间： | 2011-04-19 |
BRACHISTOCHRONE WITH VISCOUS RESISTANCE |
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| BRACHISTOCHRONE WITH VISCOUS RESISTANCE[J]. Mechanics in Engineering, 2011, 33(3): 11-14. doi: 10.6052/1000-0879-lxysj2011-123 |
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| Authors: | ZHOU Jiawei CAO Bingyang GUO Zengyuan |
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| Affiliation: | ZHOU Jiawei CAO Bingyang~(2)) GUO Zengyuan (Department of Engineering Mechanics,Tsinghua University,Beijing 100084,China) |
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| Abstract: | The brachistochrone with consideration of viscous resistance may be an issue in engineering situations. A generalized variational principle with constraints removed is deduced first,and it is also applicable to other forms of resistance and optimization of systems with multiple degrees of freedom.We then obtain the ordinary differential equations describing the functions of the brachistochrone with viscous resistance,whose solution is reduced to roulette when the viscous resistance is neglected.The effects ... |
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| Keywords: | brachistochrone viscous resistance generalized variational principle Lagrangian multiplier method |
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