摘要
首先通过对人体4个生理参数和风力的分析,由牛顿第二定律建立了赛跑的最优速度模型与能量消耗模型;其次利用微分方程的解曲线与最优控制方法,结合普通极值与泛函极值方法,给出时间一定情况下的最大距离,以及赛跑距离一定情况下的最小时间,并利用最小二乘法对若干生理参数进行拟合估计;最后以某高校40多年男子赛跑成绩为依据进行模型检验,找出理论值与实际纪录值的相对误差,从而为提高赛跑成绩提供了科学依据.
An optimum race velocity model and an energy fever model is presented based on the Newton′s second law and the analysis of wind-force and the four physiological parameters of human body. The maximum distance under the given time and the minimum time under the given distance are calculated by using the solution curve of the differential equations and the optimal control method, combining with the methods of the general extreme value and functional extreme value. Some physiological parameters are estimated by using the least squares method. The model is tested by taking the man race score in the past 40 years, and the relatively errors of the theoretical values and the real record are presented.
出处
《控制与决策》
EI
CSCD
北大核心
2004年第2期199-203,共5页
Control and Decision
基金
国家自然科学基金资助项目(69974032)
山东省自然科学基金资助项目(Q99G06).
关键词
赛跑
最大距离
最小时间
数学模型
速度控制
race
maximum distance
minimum time
mathematical model
velocity control
