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[.a] Saving screenshot @8) [Solution manual] classic (€% Search a) co Q SlideShare Explore ames) Tela # Like Therefore our equations of motion are K (ax + by) ak +h A(he + cy) = mi he + Examining the particular cases, we find. Ife =0=c ther Kr = mi Ky The physical system is harmonic oscillation of a particle of mass m in two dimensia If you ea substitution to go to a different coordinate system this is easier to see. The system can now be more easily seen as two independent but identical simple harmonic oscil. 1B, # a point transformation was made. When the condition & ac = 0 is violated, then we have 6 = ,/ac, and L’ Simplifies to this: + fey)? Note that this is mow a one dimensional problem. So the condition keeps the Lagrangian in two dimensions, or you can say that the transformation matrix is singliuar because b* if this condition holds then we can reduce the Lagrangian by a point transformation 19. Obtain the Lagrange equations of motion for spherical pendulum, ie, a Tha point suspended by a rigid weightless pod, 15 
