# American Institute of Mathematical Sciences

2007, 2007(Special): 655-666. doi: 10.3934/proc.2007.2007.655

## Hamiltonian dynamics of atom-diatomic molecule complexes and collisions

 1 University of Southern California, Department of Mathematics, KAP 108, 3620 Vermont Avenue, Los Angeles, CA 90089-2532, United States

Received  September 2006 Revised  February 2007 Published  September 2007

For a polyatomic molecule at zero total angular momentum, this paper shows that an internal motion with nonzero internal angular momentum within a (generalized) Eckart frame will produce a net rotation of the (generalized) Eckart frame in the center-of-mass frame. For a polyatomic molecule at nonzero total angular momentum, an internal motion within a generalized Eckart frame with nonzero orbital angular momentum will produce a net rotation of the generalized Eckart frame in the center-of-mass frame. Specifically, at zero total angular momentum, an internal rotation of a diatomic molecule within an atom-diatomic molecule system has nonzero internal rotational angular momentum and produces a counter-rotary net rotation of the orientation of the system (and of its generalized Eckart frame) in the center-of mass frame. Beyond a net overall rotation of an atom-diatomic molecule complex in the center-of-mass frame, a net rotation of the scattering angle of an atom colliding with a rotating diatomic molecule is obtained. A rotation in the recoil angle of an atom departing from a dissociating triatomic molecule has been observed.
Citation: F. J. Lin. Hamiltonian dynamics of atom-diatomic molecule complexes and collisions. Conference Publications, 2007, 2007 (Special) : 655-666. doi: 10.3934/proc.2007.2007.655
 [1] Hildeberto E. Cabral, Zhihong Xia. Subharmonic solutions in the restricted three-body problem. Discrete & Continuous Dynamical Systems, 1995, 1 (4) : 463-474. doi: 10.3934/dcds.1995.1.463 [2] Edward Belbruno. Random walk in the three-body problem and applications. Discrete & Continuous Dynamical Systems - S, 2008, 1 (4) : 519-540. doi: 10.3934/dcdss.2008.1.519 [3] Richard Moeckel. A topological existence proof for the Schubart orbits in the collinear three-body problem. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 609-620. doi: 10.3934/dcdsb.2008.10.609 [4] Mitsuru Shibayama. Non-integrability of the collinear three-body problem. Discrete & Continuous Dynamical Systems, 2011, 30 (1) : 299-312. doi: 10.3934/dcds.2011.30.299 [5] Jungsoo Kang. Some remarks on symmetric periodic orbits in the restricted three-body problem. Discrete & Continuous Dynamical Systems, 2014, 34 (12) : 5229-5245. doi: 10.3934/dcds.2014.34.5229 [6] Richard Moeckel. A proof of Saari's conjecture for the three-body problem in $\R^d$. Discrete & Continuous Dynamical Systems - S, 2008, 1 (4) : 631-646. doi: 10.3934/dcdss.2008.1.631 [7] Hiroshi Ozaki, Hiroshi Fukuda, Toshiaki Fujiwara. Determination of motion from orbit in the three-body problem. Conference Publications, 2011, 2011 (Special) : 1158-1166. doi: 10.3934/proc.2011.2011.1158 [8] Kuo-Chang Chen. On Chenciner-Montgomery's orbit in the three-body problem. Discrete & Continuous Dynamical Systems, 2001, 7 (1) : 85-90. doi: 10.3934/dcds.2001.7.85 [9] Chjan C. Lim, Joseph Nebus, Syed M. Assad. Monte-Carlo and polyhedron-based simulations I: extremal states of the logarithmic N-body problem on a sphere. Discrete & Continuous Dynamical Systems - B, 2003, 3 (3) : 313-342. doi: 10.3934/dcdsb.2003.3.313 [10] Nai-Chia Chen. Symmetric periodic orbits in three sub-problems of the $N$-body problem. Discrete & Continuous Dynamical Systems - B, 2014, 19 (6) : 1523-1548. doi: 10.3934/dcdsb.2014.19.1523 [11] Regina Martínez, Carles Simó. On the stability of the Lagrangian homographic solutions in a curved three-body problem on $\mathbb{S}^2$. Discrete & Continuous Dynamical Systems, 2013, 33 (3) : 1157-1175. doi: 10.3934/dcds.2013.33.1157 [12] Xiaojun Chang, Tiancheng Ouyang, Duokui Yan. Linear stability of the criss-cross orbit in the equal-mass three-body problem. Discrete & Continuous Dynamical Systems, 2016, 36 (11) : 5971-5991. doi: 10.3934/dcds.2016062 [13] Rongchang Liu, Jiangyuan Li, Duokui Yan. New periodic orbits in the planar equal-mass three-body problem. Discrete & Continuous Dynamical Systems, 2018, 38 (4) : 2187-2206. doi: 10.3934/dcds.2018090 [14] Niraj Pathak, V. O. Thomas, Elbaz I. Abouelmagd. The perturbed photogravitational restricted three-body problem: Analysis of resonant periodic orbits. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 849-875. doi: 10.3934/dcdss.2019057 [15] Abimael Bengochea, Manuel Falconi, Ernesto Pérez-Chavela. Horseshoe periodic orbits with one symmetry in the general planar three-body problem. Discrete & Continuous Dynamical Systems, 2013, 33 (3) : 987-1008. doi: 10.3934/dcds.2013.33.987 [16] Hadia H. Selim, Juan L. G. Guirao, Elbaz I. Abouelmagd. Libration points in the restricted three-body problem: Euler angles, existence and stability. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 703-710. doi: 10.3934/dcdss.2019044 [17] Qinglong Zhou, Yongchao Zhang. Analytic results for the linear stability of the equilibrium point in Robe's restricted elliptic three-body problem. Discrete & Continuous Dynamical Systems, 2017, 37 (3) : 1763-1787. doi: 10.3934/dcds.2017074 [18] Samuel R. Kaplan, Mark Levi, Richard Montgomery. Making the moon reverse its orbit, or, stuttering in the planar three-body problem. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 569-595. doi: 10.3934/dcdsb.2008.10.569 [19] Tiancheng Ouyang, Duokui Yan. Variational properties and linear stabilities of spatial isosceles orbits in the equal-mass three-body problem. Discrete & Continuous Dynamical Systems, 2017, 37 (7) : 3989-4018. doi: 10.3934/dcds.2017169 [20] Davide L. Ferrario, Alessandro Portaluri. Dynamics of the the dihedral four-body problem. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 925-974. doi: 10.3934/dcdss.2013.6.925

Impact Factor:

## Metrics

• PDF downloads (81)
• HTML views (0)
• Cited by (0)

## Other articlesby authors

• on AIMS
• on Google Scholar

[Back to Top]