Show that 2D potential flows satisfy Eulers equations even if 0 ...

Show that 2D potential flows satisfy Eulerâ€™s equations even if Î¼ â‰ 0.

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Mechanical Engineering

Show that 2D potential flows satisfy Eulerâ€™s equations even if Î¼â‰ 0.

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we learn that when an external torque acts on a body its angularmomentum changes and if no external torques act on a body itsangular momentum does not change We learn that the rate of changeof angular momentum is equal to the applied torque In the firstsimple examples that we typically meet a symmetrical body isrotating about an axis of symmetry and the torque is also appliedabout this same axis The angular momentum is just II and so thestatement that torque equals rate of change of angular momentum ismerely II and thats all there is to itLater we learn that LL II where ll is a tensor and LL and are not parallel There are three principal moments of inertiaand LL and the applied torque each have three componentsand the statement torque equals rate of change of angularmomentum somehow becomes much less easyEulers Equations sort this out and give us a relation betweenthe components of the ll and For Figure IV5 I have just reproduced with some smallmodifications Figure III19 from my notes on this Web site onCelestial Mechanics where I defined Eulerian anglesAgain it is suggested that those who are unfamiliar with Eulerianangles consult Chapter III of Celestial MechanicsIn Figure IV5 OxyzOxyz are spacefixed axes andOx0y0z0Ox0y0z0 are the bodyfixed principal axes The axisOy0Oy0 is behind the plane of your See Answer

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