Spring 2003 Generalized forces revisited Derived Lagrange s equation from d'Alembert's equation ∑m(8x+16y+22)=∑(Fx+F+F。=) Define virtual displacements sx Substitute in and noting the independence of the 8q,, for each
Spring 2003 Derivation of lagrangian equations Basic Concept: Virtual Work Consider system of N particles located at(, x2, x,,.x3N )with 3 forces per particle(f. f, f..fn). each in the positive direction
Spring 2003 Example Given: Catapult rotating at a constant rate(frictionless, in the horizontal plane) Find the eom of the particle as it leaves the tube
NUMERICAL SOLUTION GIEN A COMPLEX SET of OYNAMICS (t)=F(x) WHERE F() COULD BE A NONLINEAR FUNCTION IT CAN BE IMPOSS IBLE To ACTVALLY SOLVE FoR ( ExACTLY. OEVELOP A NUMERICAL SOLUTION. CANNED CoDES HELP US THIS TN MATLAB BUT LET US CONSDER THE BASiCS
Handout 7: Lag and PI compensation Eric Feron Lag Compensation goals: Raise gain at low frequencies while leaving rossover &z higher frequencies untouched b≥0. When b=0: Add an integrator in the loop Typical lag Bode Plot
