Higher order complex Lagrangian and Hamiltonian mechanics systems

Tekkoyun, Mehmet; Görgülü, Ali

doi:10.1016/j.physleta.2006.04.049

Cited by 10 publications

(13 citation statements)

References 6 publications

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“…One easily see that the complex (paracomplex) Euler-Lagrange and Hamilton equations introduced in [4,5] are equivalent those in (10) and (21) ((25) and (27)) if a = b = 0.…”

Section: Discussionmentioning

confidence: 94%

“…Let M 4 be a Walker manifold and {x 1 , x 2 , x 3 , x 4 } be its coordinate functions. Let the semispray be the vector field X determined by 3 3 4 4 X x   and the dot indicates the derivative with respect to time t. By means of the proper almost complex structure φ given by (4), the vector field is defined by…”

Section: Lagrangian Mechanical Systemsmentioning

confidence: 99%

“…Here m i , g and h stand for mass of a mechanical system having m particles, the gravity acceleration and distance to the origin of a mechanical system on Walker manifold M 4 , respectively. Then is a map that satisfies the conditions; 1) is a Lagrangian function, 2) the function determined by 4 :…”

Section: Lagrangian Mechanical Systemsmentioning

confidence: 99%

“…where Φ indicates the symplectic form. The triple (T * Q, Φ, X) is called a Hamiltonian system on the cotangent bundle T * Q. Nowadays, there are many studies about Lagrangian and Hamiltonian dynamics, mechanics, formalisms, systems and equations [1][2][3][4][5] and there in. There are real, complex, paracomplex and other analogues.…”

Section: Introductionmentioning

confidence: 99%

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A Survey on Geometric Dynamics of 4-Walker Manifold

Tekkoyun¹

2011

JMP

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A Walker n-manifold is a semi-Riemannian n-manifold, which admits a field of parallel null r-planes, with r ≤ 2/n . It is well-known that semi-Riemannian geometry has an important tool to describe spacetime events. Therefore, solutions of some structures about 4-Walker manifold can be used to explain spacetime singularities. Then, here we present complex and paracomplex analogues of Lagrangian and Hamiltonian mechanical systems on 4-Walker manifold. Finally, the geometrical-physical results related to complex (paracomplex) mechanical systems are also discussed

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“…One easily see that the complex (paracomplex) Euler-Lagrange and Hamilton equations introduced in [4,5] are equivalent those in (10) and (21) ((25) and (27)) if a = b = 0.…”

Section: Discussionmentioning

confidence: 94%

Section: Lagrangian Mechanical Systemsmentioning

confidence: 99%

Section: Lagrangian Mechanical Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Survey on Geometric Dynamics of 4-Walker Manifold

Tekkoyun¹

2011

JMP

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“…Therefore it has an important role in differential geometry. Really, in before studies, extensions of any real, complex manifold and complex product manifold were defined and the higher order vertical, complete and horizontal lifts of functions, vector fields and 1-forms on any manifold to its extension spaces were studied in [2,3,4,5] and there in.…”

Section: Introductionmentioning

confidence: 99%

Lifts of Time Dependent Complex Hamiltonian Mechanical Systems

Tekkoyun

2009

Preprint

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In this study, firstly, the k-th order extension of complex product manifold is considered. Then the higher order vertical, complete lifts of geometric structures on product manifold to its extended spaces are given. Also higher order lifts of tensor field of type (1,1) are presented. And then extended contact manifolds are defined. Finally higher order vertical and complete lifts of time dependent complex Hamiltonian equations on contact manifold to its extensions are introduced. In conclusion, geometric meaning of Hamiltonian mechanical systems is discussed.

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Improving Hamiltonian Energy Equations on the Kähler Jet Bundles

Civelek

Aycan

Dagli

2013

Int. J. Geom. Methods Mod. Phys.

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The aim of this paper is to improve Hamiltonian energy equations for the complex jet bundles using Kähler manifolds. The coordinates on the bundle structure of Kähler manifolds have been given for real and imaginary dimensions. For given bundle structures, all fundamental geometrical properties have been investigated in Hamiltonian energy equations and applications to complex bundle structures. The improved Hamiltonian energy equations have been applied to the presented example in order to test its performance. Moreover, we have presented a new concept of velocity and time dimensions for energy movement equations. Results showed that imaginary Hamiltonian values are opposed to real Hamiltonian values in 2n dimensions. Finally, this study showed a physical application and interpretation of velocity and time dimensions in Hamiltonian energy equations for given examples.

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Higher order complex Lagrangian and Hamiltonian mechanics systems

Cited by 10 publications

References 6 publications

A Survey on Geometric Dynamics of 4-Walker Manifold

A Survey on Geometric Dynamics of 4-Walker Manifold

Lifts of Time Dependent Complex Hamiltonian Mechanical Systems

Improving Hamiltonian Energy Equations on the Kähler Jet Bundles

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