bv_cvxbook_extra_exercises

This gives us the rst constraint w2 h2 f1 r2 r2 2h the

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Unformatted text preview: ucture. A tensile structure is modeled as a set of n masses in R2 , some of which are fixed, connected by a set of N springs. The masses are in equilibrium, with spring forces, connection forces for the fixed masses, and gravity balanced. (This equilibrium occurs when the position of the masses minimizes the total energy, defined below.) We let (xi , yi ) ∈ R2 denote the position of mass i, and mi > 0 its mass value. The first p masses fixed are fixed, which means that xi = xfixed and yi = yi , for i = 1, . . . , p. The gravitational potential i energy of mass i is gmi yi , where g ≈ 9.8 is the gravitational acceleration. Suppose spring j connects masses r and s. Its elastic potential energy is (1/2)kj (xr − xs )2 + (yr − ys )2 , where kj ≥ 0 is the stiffness of spring j . To describe the topology, i.e., which springs connect which masses, we will use the incidence matrx A ∈ Rn×N , defined as 1 head of spring j connects to mass i −1 tail of spring j connects to mass i Aij = 0 otherwise. Here we arbitrarily choose a head and t...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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