16.61 Aerospace Dynamics S 2003 Recall SW=F Ss. Two nonconservative components, look at each component in turn o Damper: W=-cqoq o Friction force δW=-sgn(q)NSq sgn(qmg cos eoq TotalⅤ irtual work 8W=(cq-sgn( q)umg cos0)&q The generalized force is thus W (cq-sgn( q)umg cos 0) O e And the eom is mq+kg -mg sin 0=-cq-sgn(qumg cos 6 =mq+cq+kg=mg(sin 8-sgn(q)ucos 0) Massachusetts Institute of Technology C How, Deyst 2003 (Based on Notes by Blair 2002)16.61 Aerospace Dynamics Spring 2003 • Recall δW = ⋅ F δ s q . Two nonconservative components, look at each component in turn: o Damper: δW c = − q&δ o Friction Force: sgn( ) sgn( ) cos W q N q q mg q = − = − δ µ δ µ θδ • Total Virtual Work: δW c = −( q& − sgn(q)µ θ mg cos )δ q • The generalized force is thus: ( ) sgn( ) cos r q r W Q cq q mg q = = − & − δ µ θ δ • And the EOM is: ( ) sin sgn( ) cos sin sgn( ) cos mq kq mg cq q mg mq cq kq mg q + − = − − + + = − && & && & θ µ θ ⇒ θ µ θ Massachusetts Institute of Technology © How, Deyst 2003 (Based on Notes by Blair 2002) 5