About non-maximality of the action functional
In this work first we review some cases where the action exhibits a minimal or a saddle-point criticality for velocity-independent potentials (V(x, t)) and maximum when the potential is velocity-dependent (V(x,ẋ,t)). In the following we will use the functional (“directional”) derivative of second o...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing LLC
2012-09-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/1.4747508 |
| Summary: | In this work first we review some cases where the action exhibits a minimal or a saddle-point criticality for velocity-independent potentials (V(x, t)) and maximum when the potential is velocity-dependent (V(x,ẋ,t)). In the following we will use the functional (“directional”) derivative of second order to present a mathematically rigorous proof of the non-maximality of the classical functional action for potentials V(x, t) velocity-independent. |
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| ISSN: | 2158-3226 |