16.61 Aerospace Dynamics Spring 2003 Simple example · Spring- mass system ass syster Linear spring Frictionless table m · Lagrangian L=T-V L=T-Ⅴ=Dmx · Lagranges equation d aLaL aq, a q e Do the derivatives aL d aL dL -x mmX dt( dq Put it all together d dL dL n元+kx=0 dt(d qi dc Massachusetts Institute of Technology C How, Deyst 2003( Based on notes by Blair 200216.61 Aerospace Dynamics Spring 2003 Massachusetts Institute of Technology © How, Deyst 2003 (Based on notes by Blair 2002) 5 Simple Example • Spring – mass system Spring mass system • Linear spring • Frictionless table m x k Spring mass system • Linear spring • Frictionless table m x k • Lagrangian L = T – V 1 1 2 2 L = T V 2 2 −= − mx kx
• Lagrange’s Equation 0 i i dL L dt q q   ∂ ∂   − = ∂ ∂  
• Do the derivatives i L mx q ∂ = ∂

, i d L mx dt q   ∂   = ∂ 


, i L kx q ∂ = − ∂ • Put it all together 0 i i dL L mx kx dt q q   ∂ ∂   − = += ∂ ∂  