bv_cvxbook_extra_exercises

You do not need to know the mechanics interpretation

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Unformatted text preview: ail for each spring, but in fact the springs are completely symmetric, and the choice can be reversed without any effect. (Hopefully you will discover why it is convenient to use the incidence matrix A to specify the topology of the system.) The total energy is the sum of the gravitational energies, over all the masses, plus the sum of the elastic energies, over all springs. The equilibrium positions of the masses is the point that minimizes the total energy, subject to the constraints that the first p positions are fixed. (In the equilibrium positions, the total force on each mass is zero.) We let Emin denote the total energy of the system, in its equilibrium position. (We assume the energy is bounded below; this occurs if and only if each mass is connected, through some set of springs with positive stiffness, to a fixed mass.) The total energy Emin is a measure of the stiffness of the structure, with larger Emin corresponding to stiffer. (We can think of Emin = −∞ as an infinitely...
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