| 31. | Notice the Routhian replaces the Hamiltonian and Lagrangian functions in all the equations of motion.
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| 32. | The geodesic equation of motion can alternatively be derived using the concept of parallel transport.
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| 33. | Producing the corresponding equations of motion of low-energy physics.
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| 34. | Then the equations of motion are of the form
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| 35. | This differential equation is the classic equation of motion of a charged particle in vacuum.
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| 36. | Still, the equations of motion follow from Hamilton's principle
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| 37. | This produces severe restrictions, because the equation of motion has to be a sensible one.
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| 38. | The equation of motion for this SDOF is
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| 39. | The resulting equation of motion is as follows:
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| 40. | Setting each of the summands to 0 will eventually give us our separated equations of motion.
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