Vakonomic Constraints in Higher-Order Classical Field Theory

2010 ◽  
Author(s):  
Cédric M. Campos ◽  
Manuel Asorey ◽  
Jesús Clemente-Gallardo ◽  
Eduardo Martínez ◽  
José F. Cariñena
2022 ◽  
Vol 9 (2) ◽  
pp. 136-141
Author(s):  
Amer D. Al-Oqali ◽  

Lagrangians which depend on higher-order derivatives appear frequently in many areas of physics. In this paper, we reformulate Podolsky's Lagrangian in fractional form using left-right Riemann-Liouville fractional derivatives. The equations of motion are obtained using the fractional Euler Lagrange equation. In addition, the energy stress tensor and the Hamiltonian are obtained in fractional form from the Lagrangian density. The resulting equations are very similar to those found in classical field theory.


Author(s):  
Jędrzej Śniatycki

AbstractGeometric structure of classical field theory in Lagrangian formulation is investigated. Symmetry transformations with generators depending on higher-order derivatives are considered and the corresponding conservation laws are obtained.


1996 ◽  
Vol 77 (20) ◽  
pp. 4109-4113 ◽  
Author(s):  
Ian M. Anderson ◽  
Charles G. Torre

2009 ◽  
Vol 64 (1) ◽  
pp. 16-47
Author(s):  
Mark Noble

This essay argues that Ralph Waldo Emerson's interest in the cutting-edge science of his generation helps to shape his understanding of persons as fluid expressions of power rather than solid bodies. In his 1872 "Natural History of Intellect," Emerson correlates the constitution of the individual mind with the tenets of Michael Faraday's classical field theory. For Faraday, experimenting with electromagnetism reveals that the atom is a node or point on a network, and that all matter is really the arrangement of energetic lines of force. This atomic model offers Emerson a technology for envisioning a materialized subjectivity that both unravels personal identity and grants access to impersonal power. On the one hand, adopting Faraday's field theory resonates with many of the affirmative philosophical and ethical claims central to Emerson's early essays. On the other hand, however, distributing the properties of Faraday's atoms onto the properties of the person also entails moments in which materialized subjects encounter their own partiality, limitation, and suffering. I suggest that Emerson represents these aspects of experience in terms that are deliberately discrepant from his conception of universal power. He presumes that if every experience boils down to the same lines of force, then the particular can be trivialized with respect to the general. As a consequence, Emerson must insulate his philosophical assertions from contamination by our most poignant experiences of limitation. The essay concludes by distinguishing Emersonian "Necessity" from Friedrich Nietzsche's similar conception of amor fati, which routes the affirmation of fate directly through suffering.


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