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I have the metric tensor $g_{\mu\nu}$. I want to make the variation of $\sqrt{-g}$ where $g=detg_{\mu\nu}$.
How can I make this work? My attempt is the following:
$$\sqrt{-g}=\sqrt{-e^{Tr(log(g_{\mu\nu}))}}=\sqrt{-e^{-Tr(log(g^{\mu\nu}))}}$$
$$\rightarrow\delta\sqrt{-g}=\delta(\sqrt{-e^{-Tr(l...
Un torseur est un outil mathématique utilisé principalement en mécanique du solide indéformable, pour décrire les mouvements des solides et les actions mécaniques qu'ils subissent de la part d'un environnement extérieur.
== Approche par la mécanique ==
Un certain nombre de vecteurs utilisés en mécanique sont des moments : moment d'une force, moment cinétique, moment dynamique. Les champs de moments possèdent des propriétés communes, et peuvent être modélisés par un même objet mathématique appelé « torseur ».
Si l'on s'intéresse au modèle du solide indéformable, le fait que la distance entre deux...
Screw theory is the algebraic calculation of pairs of vectors, such as forces and moments or angular and linear velocity, that arise in the kinematics and dynamics of rigid bodies. The mathematical framework was developed by Sir Robert Stawell Ball in 1876 for application in kinematics and statics of mechanisms (rigid body mechanics).Screw theory provides a mathematical formulation for the geometry of lines which is central to rigid body dynamics, where lines form the screw axes of spatial movement and the lines of action of forces. The pair of vectors that form the Plücker coordinates of a line...
M. P. Appell is the same person: it stands for Monsieur Paul Appell.Paul Émile Appell (27 September 1855, in Strasbourg – 24 October 1930, in Paris) was a French mathematician and Rector of the University of Paris. Appell polynomials and Appell's equations of motion are named after him, as is rue Paul Appell in the 14th arrondissement of Paris and the minor planet 988 Appella.
== Life ==
Paul Appell entered the École Normale Supérieure in 1873.
He was elected to the French Academy of Sciences in 1892.
In 1895, he became a Professor at the École Centrale Paris. Between 1903 and 1920 he was Dean...
