Asymptotic modelling in fluid mechanics : proceedings of a by Pierre-Antoine Bois; Jean-Pierre Guiraud; et al

By Pierre-Antoine Bois; Jean-Pierre Guiraud; et al

The aim of this publication is to assemble contributions from scientists in fluid mechanics who use asymptotic ways to focus on tricky difficulties. the chosen issues are as follows: vorticity and turbulence, hydrodynamic instability, non-linear waves, aerodynamics and rarefied gasoline flows. The final bankruptcy of the booklet broadens the point of view with an outline of different concerns bearing on asymptotics, awarded in a didactic method

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Additional info for Asymptotic modelling in fluid mechanics : proceedings of a symposium in honour of Professor Jean-Pierre Guiraud, held at the Université Pierre et Marie Curie, Paris France, 20-22 April 1994

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25) can again be written as T = Te- f{q) where r e is the [n x 1] vector of external or control torques and f(q) corresponds to the torques due to friction effects. 31) it is assumed that the friction is symmetric, and it is only a function of the joint velocity. However, in many robot applications it turns out that friction also exhibits some dependence on the joint position. Here, it is also assumed that the friction effects are decoupled with respect to the joint velocities, i. e. the friction effects on the i-th joint only depend on the i-th joint velocity.

Many ways exist to develop such models. For instance one can use the Lagrangian or Hamiltonian formulation of classical mechanics [Goldstein (1980)], [Book (1984)], which leads to a description based on differential equations. A different approach, based on a network representation of physical systems, is provided by the bond-graph technique [Breedveld et al. (1991)], [Stramigioli (1998)], whose multi-domain character is very useful in mechatronics. In this book the considered dynamic models are based on the Lagrangian approach.

36) is positive definite. 19). 18), is locally uniformly ultimately bounded. 1 can be made arbitrarily small by a proper chose of £ P I , M , and thus the ultimate bound for the closed loop errors e, e, e, e, qs, qs can be made arbitrarily small. 36) depends on KPtm. 35). 39) is proportional to y2, this region can be expanded by increasing y2. Thus the uniform ultimate bounded result is semi-global. 28) imply relations between the minimum and maximum eigenvalues of Lp\, LP2, and at the same time QNm and «2 depend on the maximum eigenvalue of Lp\.

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