scholarly journals A simple, global, complementary variational principle

1970 ◽  
Vol 16 (1) ◽  
pp. 52-57 ◽  
Author(s):  
James W. Daniel
Keyword(s):  
Variational Principle ◽  
Complementary Variational Principle

Generalized Quasi-Variational Principles and Application in Nonlinear Non-Conservative Elasto-Dynamics

2008 ◽  
Vol 385-387 ◽  
pp. 577-580
Author(s):  
Tao Fan ◽  
Hai Yan Song
Keyword(s):  
Variational Principle ◽  
Initial Value Problem ◽  
Analytic Solution ◽  
Variational Principles ◽  
Initial Value ◽  
Complementary Variational Principle ◽  
Two Kinds Of Variables

The generalized quasi-variational principles with two kinds of variables of time initial value problem were established in nonlinear non-conservative elasto-dynamics. Then, the analytic solution of time initial value problem of a typical non-conservative elasto-dynamics was studied by applying the obtained quasi-complementary variational principle.

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

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