rt_polar_lag

# rt_polar_lag - rt_polar_lag.nb 1 RT Lagrage's EOM...

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(* RT *) (* Lagrage's EOM *) Apply [Clear,Names["Global`*"]]; Off[General::spell]; Off[General::spell1]; " polar coordinates - mobile reference frame " rC= {L/2, 0, 0} ; rA= {r[t], 0, 0} ; Print["rC = ",rC]; Print["rA = ",rA]; G1= {-m g Sin[theta[t]], -m g Cos[theta[t]], 0}; G2= {-m g Sin[theta[t]], -m g Cos[theta[t]], 0}; Print["G1 = G2 = ", G1]; omega= {0, 0, theta'[t]}; vA=D[rA,t]+Cross[omega,rA]; vC=D[rC,t]+Cross[omega,rC]; Print["vA = ", vA]; Print["vC = ", vC]; IO=m L^2/3; "T1= IO omega . omega/2 " T1= IO omega . omega/2 ; "T2= m vA.vA/2+IA omega . omega/2 " T2= m vA.vA/2+IA omega . omega/2 ; T=T1+T2; Print["T = T1 + T2 = ",Simplify[T]]; " left hand side of the Lagrange's equations " "d[dT/d(r')]/dt - dT/dr = " LHSr=D[D[T,r'[t]],t]-D[T,r[t]] "d[dT/d(theta')]/dt - dT/d(theta) =" LHSt=D[D[T,theta'[t]],t]-D[T,theta[t]] "generalized forces" "because is a mobile reference frame do not use" "Qr = [d(rC)/dr].G1+[d(rA)/dr].G2 DO NOT USE" "USE" "Qr = [d(vC)/d(r')].G1+[d(vA)/d(r')].G2 = " Qr=D[vC,r'[t]].G1+D[vA,r'[t]].G2

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rt_polar_lag - rt_polar_lag.nb 1 RT Lagrage's EOM...

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