The classical problems of the forced motion of a fluid particle induced by the motion of solid bodies immersed in an incompressible and nonviscous fluid of unbounded extent are solved by integrating nonlinear equations of the type:
(d2r/dt2) + P(r,t)(dr/dt)3 + Q(r,t)(dr/dt)2 + R(t)dr/dt = 0
, and
(d2r/dt2) + M(r)(dr/dt)2 + N(r,t)dr/dt + S(r,t) = 0
. The solutions of the Lagrangian equations of motion instead of the usual Euler's equations furnish better physical insight. The second integrals are evaluated in terms of both elliptic integrals and series for the problem of cylinder, and hyperelliptic integrals and series for the sphere. A systematic method of integrating nonlinear equations of this type is discussed. The problem of a half-body is also discussed.
Topics
Lagrangian mechanics, Numerical methods, Integral calculus, Fluid mechanics, Fluid dynamics
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© 1963 American Association of Physics Teachers.
1963
American Association of Physics Teachers
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