Hanging chain problem

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Hanging chain problem
State dimension: 1
Differential states: 2
Discrete control functions: 1
Interior point equalities: 2

The Hanging chain problem is concerned with finding a chain (of uniform density) of length  L suspendend between two points  a, b with minimal potential energy. (Problem taken from the COPS library)


Mathematical formulation

The problem is given by

Failed to parse (syntax error): \begin{array}{llcl} \displaystyle \min_{x, u} & x_2(t_f) \\[1.5ex] \mbox{s.t.} & \dot{x}_1 & = & u, \\ & \dot{x}_2 & = & x_1 (1+u^2)^{1/2}, \\ & \dot{x}_3 & = & (1+u^2)^{1/2), \\ \end{array}

Parameters

In this model the parameters used are \begin{array}{rcl} [t_0, t_f] &=& [0, 1],\\ (a,b) &=& (0.4, 0.2),\\ Lp &=& 4. \end{array}

Source Code

Model descriptions are available in