Lagrangian formulation of equations Space Biomedical Engineerin of motion Life Support Describes the behavior of a dynamic system in terms of work and energy stored in the system Constraint forces are automatically eliminated (an advantage and a disadvantage), called the "closed form" dynamic equations Equations are derived systematically (easier to use) qu,, qn=generalized coordinates of a dynamic system T=total kinetic energy U=total potential energy Define Lagrangian: L(a 9=T-U Equations of motion are then derived from d dl dL dt di, da e 1…,n(2-1) Q =generalized force corresponding to generalized coord qLagrangian Formulation of Equations of Motion • Describes the behavior of a dynamic system in terms of work and energy stored in the system • Constraint forces are automatically eliminated (an advantage and a disadvantage), called the “closed form” dynamic equations • Equations are derived systematically (easier to use) i i i i i i i n Q q Q i n q L q L dt d L q q q q generalize d force corresponding to generalize d coord Equations of motion are then derived from : Define Lagrangian : total potential energy total kinetic energy generalize d coordinate s of a dynamic system 1 , , ( , ) , , 1 = = = ∂ ∂ − ∂ ∂ = − = = = m D D m T U U T (2-1)