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2 Acta of Bioengineering and Biomechanics

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Optimal velocity in the race over variable slope trace

Maroński R., Samoraj P.

Acta of Bioengineering and Biomechanics

2015

Vol. 17, no. 2

149--153

The minimum-time running problem is reconsidered. The time of covering a given distance is minimized. The function that should be found is the runner’s velocity that varies with the distance. The Hill-Keller model of motion is employed. It is based on the Newton second law and an equation of power balance. The new element of the current approach is that the trace slope angle varies with the distance. The problem is formulated and solved in optimal control applying the Chebyshev direct pseudospectral method. The essential finding is that the optimal velocity during the cruise is constant regardless of the local slope of the terrain. Such result is valid if the inequality constraints imposed on the propulsive force or the energy are not active.

Minimum-time running: a numerical approach

Maroński R., Rogowski K.

Acta of Bioengineering and Biomechanics

2011

Vol. 13, no. 2

83-86

The article deals with the minimum-time running problem. The time of covering a given distance is minimized. The Hill-Keller model of running employed is based on Newton's second law and the equation of power balance. The problem is formulated in optimal control. The unknown function is the runner's velocity that varies with the distance. The problem is solved applying the direct Chebyshev's pseudospectral method.