16.61 Aerospace Dynamics Spring 2003 Define: Lagrangian Function .L=T-V(Kinetic-Potential energies) Lagrange’ s Equation For conservative systems d/aLdL 0)g Results in the differential equations that describe the equations of motion of the system Key point: Newton approach requires that you find accelerations in all 3 directions, equate F=ma, solve for the constraint forces and then eliminate these to reduce the problem to characteristic size Lagrangian approach enables us to immediately reduce the problem to this"characteristic size, we only have to solve for that many equations in the first place The ease of handling external constraints really differentiates the two approaches Massachusetts Institute of Technology C How, Deyst 2003( Based on notes by Blair 2002)16.61 Aerospace Dynamics Spring 2003 Massachusetts Institute of Technology © How, Deyst 2003 (Based on notes by Blair 2002) 4 Define: Lagrangian Function • L = T – V (Kinetic – Potential energies) Lagrange’s Equation • For conservative systems 0 i i dL L dt q q   ∂ ∂   − = ∂ ∂  
• Results in the differential equations that describe the equations of motion of the system Key point: • Newton approach requires that you find accelerations in all 3 directions, equate F=ma, solve for the constraint forces, and then eliminate these to reduce the problem to “characteristic size” • Lagrangian approach enables us to immediately reduce the problem to this “characteristic size”
we only have to solve for that many equations in the first place. The ease of handling external constraints really differentiates the two approaches