Time evolution of a closed circular string

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Reference no: EM13967995

Time evolution of a closed circular string.

At t = 0, a closed string forms a circle of radi us R on the (x , y) plane and has zero veloci ty. The ti me development of this string can be studied usi ng the action (6.88). The string will remai n circular, but its radi us wi ll be a time-dependent function R( t ). Give the Lagrangian L as a function of R(t ) and i ts time derivative. Calculate the radius and velocity as functions of ti me. Sketch the spacetime surface traced by the string in a three-di mensional plot with x , y , and ct axes. [Hint: Calculate the Hamiltonian associated with L and use energy conservation.]

Reference no: EM13967995

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