Show that the function S = (mω/2)(q2 + α2) cot ωt − mωqα csc ωt is a solution of the Hamilton-Jacobi for Hamilton’s principal function for the linear harmonic oscillator with H =(1/2m)(p2 + m2ω2q2). Show that this function generates a correct solution to the motion of the harmonic oscillator.
Show that the function S = (mω/2)(q2 + α2) cot ωt − mωqα csc ωt is a solution of the Hamilton-Jacobi for Hamilton’s principal function for the linear harmonic oscillator with H =(1/2m)(p2 + m2ω2q2). Show that this function generates a correct solution to the motion of the harmonic oscillator.
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Show that the function
S = (mω/2)(q2 + α2) cot ωt − mωqα csc ωt
is a solution of the Hamilton-Jacobi for Hamilton’s principal function for the
linear harmonic oscillator with
H =(1/2m)(p2 + m2ω2q2).
Show that this function generates a correct solution to the motion of the
harmonic oscillator.
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