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The Lagrangian and Eulerian specifications of the kinematics and dynamics of the flow field are related by the material derivative (also called the Lagrangian derivative, convective derivative, substantial derivative, or particle derivative). [1] Suppose we have a flow field u, and we are also given a generic field with Eulerian specification F ...
In continuum mechanics, the material derivative [1] [2] describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field. The material derivative can serve as a link between Eulerian and Lagrangian descriptions of continuum ...
In 2004, Raffles Design Institute received the Singapore Quality Class Award for Private Education Organizations, ensuring that all courses were registered with the appropriate bodies. In 2005, the CaseTrust for Education Award for Private Education Organizations was awarded, which is an indication of approval by The Consumer Association of ...
Derivation of the Lagrangian and Eulerian finite strain tensors A measure of deformation is the difference between the squares of the differential line element d X {\displaystyle d\mathbf {X} \,\!} , in the undeformed configuration, and d x {\displaystyle d\mathbf {x} \,\!} , in the deformed configuration (Figure 2).
The derivative of a field with respect to a fixed position in space is called the Eulerian derivative, while the derivative following a moving parcel is called the advective or material (or Lagrangian [2]) derivative. The material derivative is defined as the linear operator:
The Euler–Lagrange equation was developed in connection with their studies of the tautochrone problem. The Euler–Lagrange equation was developed in the 1750s by Euler and Lagrange in connection with their studies of the tautochrone problem. This is the problem of determining a curve on which a weighted particle will fall to a fixed point in ...
A Lagrangian density L (or, simply, a Lagrangian) of order r is defined as an n-form, n = dim X, on the r-order jet manifold J r Y of Y. A Lagrangian L can be introduced as an element of the variational bicomplex of the differential graded algebra O ∗ ∞ ( Y ) of exterior forms on jet manifolds of Y → X .
Lagrangian ocean analysis makes use of the relation between the Lagrangian and Eulerian specifications of the flow field, namely (,) = ((,),) = (,), where (,) defines the trajectory of a particle (fluid parcel), labelled , as a function of the time , and the partial derivative is taken for a given fluid parcel . [6]