Symplectic reduction of higher order Lagrangian systems with symmetry

1994 ◽  
Vol 35 (12) ◽  
pp. 6546-6556 ◽  
Author(s):  
M. de León ◽  
Paulo Pitanga ◽  
P. R. Rodrigues
Keyword(s):  
Higher Order ◽  
Symplectic Reduction ◽  
Lagrangian Systems ◽  
Higher Order Lagrangian

Symmetries and constants of the motion for higher‐order Lagrangian systems

1995 ◽  
Vol 36 (8) ◽  
pp. 4138-4161 ◽  
Author(s):  
Manuel de León ◽  
David Martín de Diego
Keyword(s):  
Higher Order ◽  
Lagrangian Systems ◽  
Higher Order Lagrangian

scholarly journals Higher-order Lagrangian perturbative theory for the Cosmic Web

2014 ◽  
Vol 11 (S308) ◽  
pp. 119-120
Author(s):  
Takayuki Tatekawa ◽  
Shuntaro Mizuno
Keyword(s):  
Perturbation Theory ◽  
Fourth Order ◽  
Initial Conditions ◽  
Higher Order ◽  
Order Perturbation ◽  
Initial Condition ◽  
The Difference ◽  
Fifth Order ◽  
The Universe ◽  
Higher Order Lagrangian

AbstractZel'dovich proposed Lagrangian perturbation theory (LPT) for structure formation in the Universe. After this, higher-order perturbative equations have been derived. Recently fourth-order LPT (4LPT) have been derived by two group. We have shown fifth-order LPT (5LPT) In this conference, we notice fourth- and more higher-order perturbative equations. In fourth-order perturbation, because of the difference in handling of spatial derivative, there are two groups of equations. Then we consider the initial conditions for cosmological N-body simulations. Crocce, Pueblas, and Scoccimarro (2007) noticed that second-order perturbation theory (2LPT) is required for accuracy of several percents. We verify the effect of 3LPT initial condition for the simulations. Finally we discuss the way of further improving approach and future applications of LPTs.

scholarly journals A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for solid dynamics

2019 ◽  
Vol 353 ◽  
pp. 467-490 ◽  
Author(s):  
Evan J. Lieberman ◽  
Xiaodong Liu ◽  
Nathaniel R. Morgan ◽  
Darby J. Luscher ◽  
Donald E. Burton
Keyword(s):  
Discontinuous Galerkin ◽  
Higher Order ◽  
Hydrodynamic Method ◽  
Solid Dynamics ◽  
Higher Order Lagrangian

On the problem of stability for higher-order derivative Lagrangian systems

1987 ◽  
Vol 14 (4) ◽  
pp. 311-319 ◽  
Author(s):  
Enrico Pagani ◽  
Giampietro Tecchiolli ◽  
Sergio Zerbini
Keyword(s):  
Higher Order ◽  
Order Derivative ◽  
Lagrangian Systems ◽  
Higher Order Derivative
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