| 41. | The governing finite difference equations of motion are
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| 42. | Then we obtain the equations of motion.
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| 43. | The Euler Lagrange equations of motion are
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| 44. | The resulting classical equations of motion are:
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| 45. | The small perturbation equations of motion are:
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| 46. | Quantum field theory uses this same Lagrangian procedure to determine the equations of motion for quantum fields.
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| 47. | The equations of motion in Hamiltonian mechanics take this form if the Hamiltonian is of the form
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| 48. | Euler and Lagrange had made a practical approximation by ignoring small terms in the equations of motion.
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| 49. | The equations of motion are now:
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| 50. | The general equation of motion is:
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