The art to keep in touch: The ''good use'' of Lagrange multipliers

Physically-based modeling for computer animation allows to produce more realistic motions in less time without requiring the expertise of skilled animators. But, a computer animation is not only a numerical simulation based on classical mechanics since it follows a precise story-line. One common way to define aims in an animation is to add geometric constraints. There are several methods to manage these constraints within a physically-based framework. In this paper, we present an algorithm for constraints handling based on Lagrange multipliers. After few remarks on the equations of motion that we use, we present a first algorithm proposed by Platt. We show with a simple example that this method is not reliable. Our contribution consists in improving this algorithm to provide an efficient and robust method to handle simultaneous active constraints.

Aloys Ander als Johann von Leyden, Anne Caroline de LaGrange als Fides, Josef Draxler als Zacharie, Gustav Hölzel als Mathisen, Heinrich Kreuzer als Jonas, Rollenbild, Gruppenbildnis, in: Giacomo Meyerbeer: Le Prophète

Signatur des Originals: S 36/G12658

The Zero-Removing Property and Lagrange-Type Interpolation Series

The classical Kramer sampling theorem, which provides a method for obtaining orthogonal sampling formulas, can be formulated in a more general nonorthogonal setting. In this setting, a challenging problem is to characterize the situations when the obtained nonorthogonal sampling formulas can be expressed as Lagrange-type interpolation series. In this article a necessary and sufficient condition is given in terms of the zero removing property. Roughly speaking, this property concerns the stability of the sampled functions on removing a finite number of their zeros.

Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces of entire functions which includes as a particular case the classical Shannon sampling theory. This abstract setting allows us to obtain a sort of converse result and to characterize when the sampling formula associated with an analytic Kramer kernel can be expressed as a Lagrange-type interpolation series. On the other hand, the de Branges spaces of entire functions satisfy orthogonal sampling formulas which can be written as Lagrange-type interpolation series. In this work some links between all these ideas are established.

A second order in time modified Lagrange-Galerkin finite element method for the incompressible Navier-Stokes equations

We introduce a second order in time modified Lagrange--Galerkin (MLG) method for the time dependent incompressible Navier--Stokes equations. The main ingredient of the new method is the scheme proposed to calculate in a more efficient manner the Galerkin projection of the functions transported along the characteristic curves of the transport operator. We present error estimates for velocity and pressure in the framework of mixed finite elements when either the mini-element or the $P2/P1$ Taylor--Hood element are used.

Sampling associated with resolvent-type kernels and lagrange-type interpolation series

In this paper a new class of Kramer kernels is introduced, motivated by the resolvent of a symmetric operator with compact resolvent. The article gives a necessary and sufficient condition to ensure that the associ- ated sampling formula can be expressed as a Lagrange-type interpolation series. Finally, an illustrative example, taken from the Hamburger moment problem theory, is included.

History and general catalogue of LaGrange Collegiate Institute : situated at Ontario, LaGrange Co., Ind.

Mode of access: Internet.

On N-dimensional Taylor and Lagrange operators /

"AEC Contract AT(04-3)-400."

Oeuvres de Lagrange /

T. 1 - T. 2 - T. 3 -T. 4 - T. 5 - T. 6 - T. 7 -T. 8 -T. 9 - T. 10 - T. 11 - T. 12 - T. 13 - T. 14.

Journal de la Société des Pharmaciens de Paris ou recueil d'observations de chimie et de pharmacie, publié pendant les années VI, VII [et] VIII de la République par les citoyens Fourcroy, Vauquelin, Parmentier, Déyeux et Bouillon-Lagrange ... formant un volume in-quarto ...

Mode of access: Internet.

Intorno alla vita ed alle opere di Luigi Lagrange /

Discorso letto nel R. Liceo Galilei di Pisa per la Festa Letteraria Commemorativa.

Elogio di Luigi Lagrange.

Errata: p. [143].

Die Principien der höheren Analysis in ihrer Entwicklung von Liebniz bis auf Lagrange, als ein historisch-kritischer Beitrag zur Geschichte der Mathematik dargestellt,

Mode of access: Internet.

Œuvres de Lagrange,

Mode of access: Internet.

Uber Kartenprojection. Abhandlungen von Lagrange (1779) und Gauss (1822)

Mode of access: Internet.