One dimensional infinite-horizon variational problems arising in continuum mechanics

1989 ◽  
Vol 106 (2) ◽  
pp. 161-194 ◽  
Author(s):  
Arie Leizarowitz ◽  
Victor J. Mizel
Keyword(s):  
Continuum Mechanics ◽  
Infinite Horizon ◽  
Variational Problems ◽  
One Dimensional

scholarly journals Cosmic Analogues of Classic Variational Problems

Universe ◽  
2020 ◽  
Vol 6 (6) ◽  
pp. 71 ◽  
Author(s):  
Valerio Faraoni
Keyword(s):  
Relativistic Particle ◽  
Friedmann Equation ◽  
Variational Calculus ◽  
Variational Problems ◽  
Particle Mechanics ◽  
One Dimensional ◽  
Spatially Homogeneous

Several classic one-dimensional problems of variational calculus originating in non-relativistic particle mechanics have solutions that are analogues of spatially homogeneous and isotropic universes. They are ruled by an equation which is formally a Friedmann equation for a suitable cosmic fluid. These problems are revisited and their cosmic analogues are pointed out. Some correspond to the main solutions of cosmology, while others are analogous to exotic cosmologies with phantom fluids and finite future singularities.

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