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Soft Constraint Octave Script
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% This tests a two particle mass-spring-damper system with particle 1 connect to ground and | |
% particle 2 connected to particle 1. Particle 2 is much heavier than particle 1 and the | |
% simulation can go unstable if the soft constraint is made too stiff. | |
% Stability is improved by adding a relaxation step that applies the rigid constraint after | |
% the position update. | |
% no relax stable up to 13.5 Hz | |
% with relax stable up to 20.5 Hz | |
relax = 1; | |
hertz = 20.5; | |
ys = [0;-1]; | |
vs = [0;0]; | |
ms = [0.167;0.000995]; | |
km = [ms(1);ms(1) + ms(2)]; | |
em = [1/km(1); 1/km(2)]; | |
h = 1/60; | |
% no damping | |
zeta = 0; | |
omega = 2 * pi * hertz; | |
biasCoeff = omega / (2 * zeta + h * omega); | |
c = h * omega * (2 * zeta + h * omega); | |
impulseCoeff = 1 / (1 + c); | |
massCoeff = c * impulseCoeff; | |
lambdas = [0;0]; | |
yys = [ys]; | |
for i = 1:10000 | |
vs(1) += -10 * h; | |
vs(2) += -10 * h; | |
% warm start | |
vs(1) += ms(1) * (lambdas(1) - lambdas(2)); | |
vs(2) += ms(2) * lambdas(2); | |
cdot1 = vs(1); | |
c1 = ys(1); | |
bias = biasCoeff * c1; | |
lambda1 = -massCoeff * em(1) * (cdot1 + bias) - impulseCoeff * lambdas(1); | |
lambdas(1) += lambda1; | |
vs(1) += ms(1) * lambda1; | |
cdot2 = vs(2) - vs(1); | |
c2 = ys(2) - ys(1) + 1; | |
lambda2 = -massCoeff * em(2) * (cdot2 + biasCoeff * c2) - impulseCoeff * lambdas(2); | |
lambdas(2) += lambda2; | |
vs(1) -= ms(1) * lambda2; | |
vs(2) += ms(2) * lambda2; | |
ys(1) += h * vs(1); | |
ys(2) += h * vs(2); | |
% relax | |
if relax == 1 | |
cdot1 = vs(1); | |
lambda1 = -em(1) * cdot1; | |
lambdas(1) += lambda1; | |
vs(1) += ms(1) * lambda1; | |
cdot2 = vs(2) - vs(1); | |
lambda2 = -em(2) * cdot2; | |
lambdas(2) += lambda2; | |
vs(1) -= ms(1) * lambda2; | |
vs(2) += ms(2) * lambda2; | |
end | |
yys = [yys ys]; | |
end | |
plot(yys') |
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