Problem motion. is mous m in a central potential A particle of that does not...
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Problem motion. is mous m in a central potential A particle of ✓ that does not depend on velocity. Find the integrals V maing of motion. solution for the given system, in spherical cond. the the system is K.E. of On finding the integrals of T= m 2 V is independent of vel. For such potential IV-0₁ the 29 2-dependent potential gives the Lagrandian To find the Hamiltonian, H={P. 9₁ - L 9. evaluate b = OL - OT_aV y 291 =k 29. og. dg. moment a 2 2 ( ₁² + 2²0² + 1² sin ²0 4² ) or writing 2 → p₂ = D I = mr, P = 0I = m²o $ po ₂0 T = m² di 各 'd 2 2 L2 H = ± √b² + P²³² + P²₂² 2ml = 2 = H = m₂ ² + m₁²0² + m ²² sims 4 + V 2 2 2² 2² simo. Date: Therefore, the Hamiltonian becomes A-pritpopo-L H = (mi) i + (m ²³ ó) ó Hm { "Sin of) 4 04) 2 it in terms of + от 29. =OT = mr²² Sinod + V (r). have to Smart notes Scanned with CamScanner - mitmistmismod 2 2 -v} the conjugate 2 2 (2+H] [E+ H PH 1 #7 Now me thy different quantities by taking their Poisson brackets with the Hamiltonian to find if they are constants (integrals) of motion. • Solve [P₂H]. [Po. Problem motion. is mous m in a central potential A particle of ✓ that does not depend on velocity. Find the integrals V maing of motion. solution for the given system, in spherical cond. the the system is K.E. of On finding the integrals of T= m 2 V is independent of vel. For such potential IV-0₁ the 29 2-dependent potential gives the Lagrandian To find the Hamiltonian, H={P. 9₁ - L 9. evaluate b = OL - OT_aV y 291 =k 29. og. dg. moment a 2 2 ( ₁² + 2²0² + 1² sin ²0 4² ) or writing 2 → p₂ = D I = mr, P = 0I = m²o $ po ₂0 T = m² di 各 'd 2 2 L2 H = ± √b² + P²³² + P²₂² 2ml = 2 = H = m₂ ² + m₁²0² + m ²² sims 4 + V 2 2 2² 2² simo. Date: Therefore, the Hamiltonian becomes A-pritpopo-L H = (mi) i + (m ²³ ó) ó Hm { "Sin of) 4 04) 2 it in terms of + от 29. =OT = mr²² Sinod + V (r). have to Smart notes Scanned with CamScanner - mitmistmismod 2 2 -v} the conjugate 2 2 (2+H] [E+ H PH 1 #7 Now me thy different quantities by taking their Poisson brackets with the Hamiltonian to find if they are constants (integrals) of motion. • Solve [P₂H]. [Po.
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Related Book For
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
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