A Treatise On Dynamics, With Examples And Exercises
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35], who also remarks that the value of the time of passage would not be altered if terms k"v^ + k"'v'^+ ... were added to the resistance.
The discussion here given is a version of Eouth's modification of Laplace's process for the case of the resisted motion of a particle under gravity. [Laplace, loc. cit., Routh, El. Rigid Dynamics, § 492.] §§ 98, 99] BRACHISTOCHKONES.
17& Ex. 9. If in the last example the impressed force P be due to gravity we get, measuring z downwards, dz Tfi , , ,, ^df -9z...=^^(e'^''-K's) + a If we suppose that k'=0, this equation becomes the equation of a cycloid. The curve in which the particle is con- strained to move must therefore be a cycloid if the impressed force be that of gravity, and there be no resistance depending on the second or higher powers of the speed. This may be compared with the result of § 97 for the cycloidal pendulum.
99. Brachistochrones. The problem of the line of quickest descent, or, to put it more generally, of the path of quickest passage, in a given field of force from one given point in the field to another, is of great interest.
What to read after A Treatise On Dynamics, With Examples And Exercises?
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To quickly assess the difficulty of the text, read a short excerpt:
35], who also remarks that the value of the time of passage would not be altered if terms k"v^ + k"'v'^+ ... were added to the resistance.
The discussion here given is a version of Eouth's modification of Laplace's process for the case of the resisted motion of a particle under gravity. [Laplace, loc. cit., Routh, El. Rigid Dynamics, § 492.] §§ 98, 99] BRACHISTOCHKONES.
17& Ex. 9. If in the last example the impressed force P be due to gravity we get, measuring z downwards, dz Tfi , , ,, ^df -9z...=^^(e'^''-K's) + a If we suppose that k'=0, this equation becomes the equation of a cycloid. The curve in which the particle is con- strained to move must therefore be a cycloid if the impressed force be that of gravity, and there be no resistance depending on the second or higher powers of the speed. This may be compared with the result of § 97 for the cycloidal pendulum.
99. Brachistochrones. The problem of the line of quickest descent, or, to put it more generally, of the path of quickest passage, in a given field of force from one given point in the field to another, is of great interest.
What to read after A Treatise On Dynamics, With Examples And Exercises?
You can find similar books in the "Read Also" column, or choose other free books by Gray, Andrew, 1847-1925 to read onlineMoreLess
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