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Hanging chain problem

From mintOC
Hanging chain problem
State dimension: 1
Differential states: 3
Continuous control functions: 1
Path constraints: 4
Interior point equalities: 5

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

minx,ux2(tf)s.t.x˙1=u,x˙2=x1(1+u2)1/2,x˙3=(1+u2)1/2,x(t0)=(a,0,0)T,x1(tf)=b,x3(tf)=Lp,x(t)[0,10],u(t)[10,20].

Parameters

In this model the parameters used are

[t0,tf]=[0,1],(a,b)=(1,3),Lp=4.

Source Code

Model descriptions are available in