Article

# Constant of motion, Lagrangian and Hamiltonian of the gravitational attraction of two bodies with variable mass

International Journal of Theoretical Physics (Impact Factor: 1.19). 12/2005; DOI: 10.1007/s10773-006-9085-4

Source: arXiv

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**ABSTRACT:**We study both classical and quantum relation between two Hamiltonian systems which are mutually connected by time-dependent canonical transformation. One is ordinary conservative system and the other is time-dependent Hamiltonian system. The quantum unitary operator relevant to classical canonical transformation between the two systems are obtained through rigorous evaluation. With the aid of the unitary operator, we have derived quantum states of the time-dependent Hamiltonian system through transforming the quantum states of the conservative system. The invariant operators of the two systems are presented and the relation between them are addressed. We showed that there exist numerous Hamiltonians, which gives the same classical equation of motion. Though it is impossible to distinguish the systems described by these Hamiltonians within the realm of classical mechanics, they can be distinguishable quantum mechanically.Communications in Theoretical Physics 09/2009; 52(3):416. · 1.05 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In a recent paper, published in Astrophys. Space Sci. (337:107, 2012) (hereafter paper ZZX) and entitled “On the triangular libration points in photogravitational restricted three-body problem with variable mass”, the authors study the location and stability of the generalized Lagrange libration points L 4 and L 5. However their study is flawed in two aspects. First they fail to write correctly the equations of motion of the variable mass problem. Second they attribute a variable mass to the third body of the restricted three-body model, a fact that is not compatible with the assumptions used in deriving the mathematical formulation of this model.Astrophysics and Space Science 06/2012; 339(2). · 2.40 Impact Factor

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