TY - GEN

T1 - Collapse

AU - Rote, Günter

AU - Zwickt, Uri

PY - 2011

Y1 - 2011

N2 - The problem of checking whether a given tower of bricks is stable can be easily answered by checking whether a system of linear inequalities has a feasible solution. A more challenging problem is to determine how an unstable tower of bricks collapses. We use Gauß' principle of least restraint to show that this, and more general rigid-body simulation problems in which many parts touch each other, can be reduced to solving a sequence of convex quadratic programs, with linear constraints, corresponding to a discretization of time. The first of these quadratic programs gives an exact description of initial infinitesimal collapse. The results of the subsequent programs need to be integrated over time to yield an approximation of the global motion of the system.

AB - The problem of checking whether a given tower of bricks is stable can be easily answered by checking whether a system of linear inequalities has a feasible solution. A more challenging problem is to determine how an unstable tower of bricks collapses. We use Gauß' principle of least restraint to show that this, and more general rigid-body simulation problems in which many parts touch each other, can be reduced to solving a sequence of convex quadratic programs, with linear constraints, corresponding to a discretization of time. The first of these quadratic programs gives an exact description of initial infinitesimal collapse. The results of the subsequent programs need to be integrated over time to yield an approximation of the global motion of the system.

UR - http://www.scopus.com/inward/record.url?scp=79955727149&partnerID=8YFLogxK

U2 - 10.1137/1.9781611973082.47

DO - 10.1137/1.9781611973082.47

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AN - SCOPUS:79955727149

SN - 9780898719932

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 603

EP - 613

BT - Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2011

PB - Association for Computing Machinery

ER -