Introduction & Motivation Introduction & Motivation Model & Simulation Model & Simulation Results Results Domain Patterns Domain Patterns Energy Terms Energy Terms Field Enhanced Piezoelectricity Field Enhanced Piezoelectricity Enhanced Piezoelectricity at Zero Field Enhanced Piezoelectricity at Zero Field Enhanced Piezoelectricity: Critical Phenomena Enhanced Piezoelectricity: Critical Phenomena Summary Summary
LECTURE+ 12 RIGID BODY OYNAAICS 工 MPLICAT IONsF GENERAL ROTATIONAL OYWMICS EJLER's EQUATIN of MOTION TORQVE FREE SPECIAL CASES. PRIMARY LESSONS: 30 ROTATONAL MOTION MUCH MORE COMPLEX THAN PLANAR (20) EULER'S E.o.M. PROVIOE STARTING POINT FoR ALL+ OYwAmIcs SOLUTINS To EvlER's EQuATIONS ARE COMPLEX BUT WE CAN OEVE LOP GooO GEOMETRIC VISUALIZATION TOOLS
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