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Variational principles of second, first and intermediate kinds for non-holonomic mechanics

Science China Mathematics 1999年第5期42卷 546-551页

作者：朱如曾 1. Laboratory for nonlinear Mechanics of Continuous Media Institute of Mechanics Chinese Academy of Sciences 100080 Beijing China

The differential variational principles of second kind for non-holonomic mechanics are given, from which a number of integral variational principles of second kind are set up. From the latter, the general relation of δq’-δq and the general form of integral variational principles of the first kind and intermediate kinds are derived. Thus not only all previous relations of δq-δq and integral variational principles are unified but also the existance of the variational principles of intermediate kinds are pointed out.

关键词： non-holonomic mechanics variational principle.

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A Novel Dynamic Obstacle Avoidance Algorithm Based on Collision Time Histogram

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Chinese Journal of Electronics 2017年第3期26卷 522-529页

作者： ZHUGE Chengchen CAI Yunfei TANG Zhenmin School of Computer Science and Engineering Nanjing University of Science and Technology

Robot path planning in uncertain dynamic environment is a hot issue in the field of Unmanned ground vehicle(UGV).Starting from the practical demands of UGV,we propose a novel dynamic obstacle avoidance algorithm based on Collision time histogram(CTH).Given current steering angle,an effective collision check model,which is called Collision check circles(CCC),is firstly *** local environment information is then combined with CCC to generate the proposed *** nonholonomic nature of the vehicle is embedded in this ***,the proposed algorithm calculates the executing steering angle by considering both the CTH and the target *** experiments and comparisons are conducted to evaluate the performance of the proposed *** experiments are firstly conducted to verify its ***,real-world experiment is conducted to verify its *** results demonstrate the practical value of the proposed algorithm.

关键词： Unmanned ground vehicle Obstacle avoidance Collision time histogram non-holonomic Collision check circles

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non-contemporaneous variations and Holder's principle

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Science China(Physics,Mechanics & Astronomy) 2003年第5期46卷 449-459页

作者：梁立孚胡海昌刘石泉 Space Engineering Department of Harbin Engineering University Harbin 150001 China Chinese Academy of Space Technology Institute of Spacecraft System Engineering Beijing 100086 China China Sanjiang Space Industry Group Corporation Wuhan 430015 China

In the process of deducing the Holder principle, a key step is to use the concept of non-contemporaneous variations. In this paper, whether starting from analytic method or from graphic solution method, the authors prove that the expression formula of non-contemporaneous variations is incorrect when the variable functions have zero-order nearness degree, and obtain a new expression. From the view of calculus of variations and differential calculus, the non-contemporaneous variations are studied. The study result shows that the concept of non-contemporaneous variations is a combination of the concept of variations and the concept of differentiation. The authors prove that the new expression is correct and obtain an equivalent expression of it. By means of this equivalent expression, this paper proves that the above expression formula of non-contemporaneous variations is correct when the variable functions have one-order nearness degree. Further study shows that, in the process of deducing Holder's principle, there is an implicit expression. Whether starting from analytic method or from graphic solution method, the authors discovered that the implicit expression of non-contemporaneous variations is incorrect when the variable functions have zero-order nearness degree and have one-order nearness degree. This paper proves that the implicit expression of non-contemporaneous variations is correct when the variable functions have two-order nearness degree. Further study shows that Holder's principle is tenable when the variable functions have two-order nearness degree.

关键词： differentiation, variation, non-contemporaneous variations, non-holonomic systems.

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