16.61 Aerospace Dynamics Spring 2003 Define generalized force Fyi oqr +F e Recall that the rhs was derived from the virtual work SW qr og Note, we can also find the effect of conservative forces using virtual work techniques as well Example Mass suspended from linear spring and velocity proportional damper slides on a plane with friction Find the equation of motion of the mass DOF=3-2 g k Constraint equations: y=2=0 q1) Generalized coordinate: q Kinetic Energy: T=mq Potential Energy: V=kq'-mggsin 8 Massachusetts Institute of Technology C How, Deyst 2003 (Based on Notes by Blair 2002)16.61 Aerospace Dynamics Spring 2003 • Define Generalized Force: 1 r i i i p i i q x y z i r r x i r y z Q F F F = q q   q ∂ ∂ ∂ = +   + ∂ ∂ ∂   ∑ • Recall that the RHS was derived from the virtual work: r q r W Q q = δ δ • Note, we can also find the effect of conservative forces using virtual work techniques as well. Example • Mass suspended from linear spring and velocity proportional damper slides on a plane with friction. • Find the equation of motion of the mass. g c k m q(t) µ θ g c k m q(t) µ θ • DOF = 3 – 2 = 1. • Constraint equations: y = z = 0. • Generalized coordinate: q • Kinetic Energy: 1 2 2 T m = q& • Potential Energy: 1 2 sin 2 V k = − q mgq θ Massachusetts Institute of Technology © How, Deyst 2003 (Based on Notes by Blair 2002) 3