Classical Mechanics - Assignment 1, Quizzes of Classical Mechanics

Download Classical Mechanics - Assignment 1 and more Quizzes Classical Mechanics in PDF only on Docsity!

WŚLJƐŝĐƐ,ŽŶŽƵƌƐ>ĞĐƚƵƌĞƐ ƐƐŝŐŶŵĞŶƚϭ

Physics Honours Lectures Assignment 1 1. Coordinate transformations (a) Consider the Lagrangian £(x,x,y,y) = din (x? + w) fora free particle in 2 dimensions (x,y). An observer sitting on a roundabout uses a rotating coordinate system (X,Y) where x = Xcoswt — Ysinwt y = Xsinwt + Y cos wt. and w is the angular velocity of roundabout. Calculate the Lagrangian in the new coordinates, £(X, X,Y,Y), and the resulting equations of motion. Identify the fictitious forces. sts Koos lk —XW Sine — Ysinwe - Ys 60s Wl > K sine +XWeoswl + Yeoswe — VUSmut atk ~ Yw) cos we — CY 4Xw) finwe H+ Ok —Yudscawe 4 (Y4kKv) ose v=-l Ya) Coste + (