16.61 Aerospace Dynamics Spring 2003 Ravleigh's Dissipation Function For systems with conservative and non-conservative forces we developed the general form of Lagrange's equation d OL aL Q with l=t-v and x Qa=Fo-+F +F qr For non-conservative forces that are a function of q, there is an alternative approach. Consider generalized forces QN=-∑cn(q where the c, are the damping coefficients, which are dissipative in nature, result in a loss of energy Now define the rayleigh dissipation function F=22∑ Ci g, g Massachusetts Institute of Technology C How, Deyst 2003 (Based on Notes by Blair 2002)16.61 Aerospace Dynamics Spring 2003 Rayleigh's Dissipation Function • For systems with conservative and non-conservative forces, we developed the general form of Lagrange's equation N qr r r d L L Q dt q q   ∂ ∂   − = ∂ ∂   & with L=T-V and r N q x y z r r x r y z Q F F F q q q ∂ ∂ ∂ = + + ∂ ∂ ∂ • For non-conservative forces that are a function of , there is an alternative approach. Consider generalized forces q& 1 ( , ) n N i ij j Q c q = = −∑ &j t q where the are the damping coefficients, which are dissipative in nature Î result in a loss of energy ij c • Now define the Rayleigh dissipation function 1 1 1 2 n n ij i j i j F c = = = ∑∑ q& &q Massachusetts Institute of Technology © How, Deyst 2003 (Based on Notes by Blair 2002) 7