By applying the methods of the calculus of variations, show that if there is a Lagrangian of the form L(qi, q˙i, q¨i, t), and Hamilton’s principle holds with the zero variation of both qi and ˙qi at the end points, then the corresponding Euler-Lagrange equations are (d2/dt2)(∂L/∂q¨i) − (d/dt)(∂L/∂q˙i) + ∂L/ ∂qi = 0, i = 1, 2, ..., n. Apply this result to the Lagrangian L = −(m/2)qq¨− (k/2)q2 . Do you recognize the equations of motion?
By applying the methods of the calculus of variations, show that if there is a Lagrangian of the form L(qi, q˙i, q¨i, t), and Hamilton’s principle holds with the zero variation of both qi and ˙qi at the end points, then the corresponding Euler-Lagrange equations are (d2/dt2)(∂L/∂q¨i) − (d/dt)(∂L/∂q˙i) + ∂L/ ∂qi = 0, i = 1, 2, ..., n. Apply this result to the Lagrangian L = −(m/2)qq¨− (k/2)q2 . Do you recognize the equations of motion?
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By applying the methods of the calculus of variations, show that if there
is a Lagrangian of the form L(qi, q˙i, q¨i, t), and Hamilton’s principle holds with the zero variation of both qi and ˙qi at the end points, then the corresponding Euler-Lagrange equations are
(d2/dt2)(∂L/∂q¨i) − (d/dt)(∂L/∂q˙i) + ∂L/ ∂qi = 0, i = 1, 2, ..., n.
Apply this result to the Lagrangian
L = −(m/2)qq¨− (k/2)q2
.
Do you recognize the equations of motion?
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