1、Introduction to Mass-Spring Systems,Graphics & Media Lab.SNU,Mass-Spring Systems,Particles (dimensionless mass points) interconnected with springs,Introduction to Elastic Springs,Spring characteristics Stiffness constant: k Initial spring length: l Current spring length: xHookes law: F = k(x - l),Fo
2、rces acting on the Mass Points,Internal forceExternal force Gravity, etc.Resulting force,Static Equilibrium,System of mass pointsStatic equilibrium,Equation for the Dynamic Movements,Equation of motion Newtons 2nd lawEquation of motion with damping,From Static Eq. to Dynamic Eq.,Static equilibriumEq
3、uation of motion,with damping,Mass-Spring Dynamics,Equation of motion for mass point i at time t2nd order differential equation f is used for acceleration and damping Without damping term, simply f = ma,mass,position,damping coefficient,spring + external,damping,acceleration,Numerical Integration,2n
4、d order ODE two coupled 1st order ODEs,velocity,acceleration,Damping Revisited,Point dampingDamping force in opposite direction to the velocityDamped springDamping force proportional to the velocity of the spring,Topology and Stability,Stability with respect to deformation,not stable,stable but not general,Requires well-chosen stable topologies!,
