Lagrangian Formulation Space Biomedical Engineerin Life Support Potential Energy U=∑mgna(2.9 Generalized forces Q=T+JF(2-10) t=joint torques JF = external forces and moments Lagrange's Equations of Motion(see Asada Slotine for derivation) ∑H4,+∑∑+G=Q(=1…)/%OHn,, j=l k= Inertia Centrifugal Gravity Generalized (2-11) G, 2m, Ji torques Coriolis trqs torque ForcesLagrangian Formulation Potential Energy ∑ = = n i ci T m i 1 0, U g r (2-9) Generalized Forces ext T Q = τ + J F τ = joint torques = external forces and moments ext T J F Lagrange’s Equations of Motion (see Asada & Slotine for derivation) H q h q qk Gi Qi (i n n j j n k j ijk n j ij 1 , , 1 1 ∑ CC +∑∑ C C + = = l = = i jk k ij ijk q H q H h ∂ ∂ − ∂ ∂ = 2 1 (2-11) (2-10) Inertia torques Centrifugal/ Coriolis trqs Gravity torque Generalized Forces ( ) 1 j Li n j T G i ∑mjg J = = ) =1