16.61 Aerospace Dynamics Spring 2003 · Lagrangian:L=T- na ka mgg sin e Derivatives OL dl aL aL ng -kg +mg sin 6 Lagrange's Equation aL aL mq+kq-mg sin=o To handle friction force in the generalized force term, need to know the normal force> Lagrange approach does not indicate the value of this force o Look at the free body diagram 7g o Since body in motion at the time of the virtual displacement, use F the d'alembert principle and include the inertia forces as well N as the real external forces o Sum forces perpendicular to the motion: N=mg cose Massachusetts Institute of Technology C How, Deyst 2003 (Based on Notes by Blair 2002)16.61 Aerospace Dynamics Spring 2003 • Lagrangian: 1 1 2 2 sin 2 2 L T = −V = mq& − kq + mgq θ • Derivatives: , , L d L L mq mq kq mg q dt q q ∂ ∂  ∂ = = = − +   ∂ ∂  ∂ & && & & sinθ • Lagrange’s Equation: sin r q d L L mq kq mg Q dt q q   ∂ ∂ − = + − =     ∂ ∂ && & θ • To handle friction force in the generalized force term, need to know the normal force Æ Lagrange approach does not indicate the value of this force. Fs mg Fd N Ff mq&& o Look at the free body diagram. o Since body in motion at the time of the virtual displacement, use the d’Alembert principle and include the inertia forces as well as the real external forces o Sum forces perpendicular to the motion: N m= g cosθ Massachusetts Institute of Technology © How, Deyst 2003 (Based on Notes by Blair 2002) 4