On Backlund transformation and motion of null Cartan curves

2021 ◽  
Author(s):  
Melek Erdoğdu ◽  
Ayşe Yavuz
Keyword(s):  
Angular Momentum ◽  
Constant Curvature ◽  
Vector Fields ◽  
Bäcklund Transformation ◽  
Position Vector ◽  
Angular Momentum Vector ◽  
Backlund Transformation ◽  
Momentum Vector ◽  
Bertrand Curve ◽  
Modern Physics

The main scope of this paper is to examine null Cartan curves especially the ones with constant torsion. In accordance with this scope, the position vector of a null Cartan curve is stated by a linear combination of the vector fields of its pseudo-orthogonal frame with differentiable functions. However, the most important difference that distinguishes this study from the other studies is that the Bertrand curve couples (timelike, spacelike or null) of null Cartan curves are also examined. Consequently, it is seen that all kinds of Bertrand couples of a given null Cartan curve with constant curvature functions have also constant curvature functions. This result is the most valuable result of the study, but allows us to introduce a transformation on null Cartan curves. Then, it is proved that aforesaid transformation is a Backlund transformation which is well recognized in modern physics. Moreover, motion of an inextensible null Cartan curve is investigated. By considering time evolution of null Cartan curve, the angular momentum vector is examined. And three different situations are given depending on the character of the angular momentum vector [Formula: see text] In the case of [Formula: see text] we discuss the solution of the system which is obtained by compatibility conditions. Finally, we provide the relation between torsion of the curve and the velocity vector components of the moving curve [Formula: see text]

scholarly journals Two Conjectures of G.D. Birkhoff

1999 ◽  
Vol 172 ◽  
pp. 439-440
Author(s):  
Christopher K. Mccord ◽  
Kenneth R. Meyer
Keyword(s):  
Angular Momentum ◽  
Integral Manifold ◽  
Center Of Mass ◽  
Angular Momentum Vector ◽  
Momentum Vector ◽  
Algebraic Set ◽  
Special Values ◽  
Integral Manifolds ◽  
Energy Center ◽  
Three Body

The spatial (planar) three-body problem admits the ten (six) integrals of energy, center of mass, linear momentum and angular momentum. Fixing these integrals defines an eight (six) dimensional algebraic set called the integral manifold, 𝔐(c, h) (m(c, h)), which depends on the energy level h and the magnitude c of the angular momentum vector. The seven (five) dimensional reduced integral manifold, 𝔐R(c, h) (mR(c, h)), is the quotient space 𝔐(c, h)/SO2 (m(c, h)/SO2) where the SO2 action is rotation about the angular momentum vector. We want to determine how the geometry or topology of these sets depends on c and h. It turns out that there is one bifurcation parameter, ν = −c2h, and nme (six) special values of this parameter, νi, i = 1, …, 9.At each of the special values the geometric restrictions imposed by the integrals change, but one of these values, ν5, does not give rise to a change in the topology of the integral manifolds 𝔐(c, h) and 𝔐R(c, h). The other eight special values give rise to nine different topologically distinct cases. We give a complete description of the geometry of these sets along with their homology. These results confirm some conjectures and refutes several others.

Impulsive formation control using orbital energy and angular momentum vector

2010 ◽  
Vol 67 (5-6) ◽  
pp. 613-622 ◽  
Author(s):  
Yoonhyuk Choi ◽  
Sunghoon Mok ◽  
Hyochoong Bang
Keyword(s):  
Angular Momentum ◽  
Formation Control ◽  
Orbital Energy ◽  
Angular Momentum Vector ◽  
Momentum Vector

scholarly journals Division I Working Group on “Precession and the Ecliptic”

2005 ◽  
Vol 1 (T26A) ◽  
pp. 67-67
Author(s):  
James L. Hilton ◽  
N. Capitaine ◽  
J. Chapront ◽  
J.M. Ferrandiz ◽  
A. Fienga ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Division I ◽  
General Assembly ◽  
Angular Momentum Vector ◽  
Inertial Reference Frame ◽  
Matrix Representations ◽  
Momentum Vector ◽  
Polynomial Coefficients ◽  
The Earth ◽  
The Mean

AbstractThe WG has conferred via email on the topics of providing a precession theory dynamically consistent with the IAU 2000A nutation theory and updating the expressions defining the ecliptic. The consensus of the WG is to recommend:(a) The terms lunisolar precession and planetary precession be replaced by precession of the equator and precession of the ecliptic, respectively.(b) The IAU adopt the P03 precession theory, of Capitaine et al (2003a, A& A 412, 567–586) for the precession of the equator (Eqs. 37) and the precession of the ecliptic (Eqs. 38); the same paper provides the polynomial developments for the P03 primary angles and a number of derived quantities for use in both the equinox based and celestial intermediate origin based paradigms.(c) The choice of precession parameters be left to the user.(d) The recommended polynomial coefficients for a number of precession angles are given in Table 1 of the WG report, including the P03 expressions set out in Tables 3–;5 of Capitaine et al (2005, A& A 432, 355–;367), and those of the alternative Fukushima (2003, AJ 126, 494–;534) parameterization; the corresponding matrix representations are given in equations 1, 6, 11, and 22 of the WG report.(e) The ecliptic pole should be explicitly defined by the mean orbital angular momentum vector of the Earth-Moon barycenter in an inertial reference frame, and this definition should be explicitly stated to avoid confusion with older definitions. The formal WG report will be submitted, shortly to Celest. Mech. for publication and their recommendations will be submitted at the next General Assembly for adoption by the IAU.

STEREODYNAMICS, MASS EFFECT AND DOCKING FROM O(3P) + HD → OH + D AT Ecol = 0.4–1.0eV AND O(3P) + HD → OD + H AT Ecol = 0.5–1.0eV

2013 ◽  
Vol 12 (01) ◽  
pp. 1250104 ◽  
Author(s):  
VICTOR WEI-KEH (WU) CHAO
Keyword(s):  
Angular Momentum ◽  
Relative Velocity ◽  
Mass Effect ◽  
Dihedral Angles ◽  
Angular Momentum Vector ◽  
Momentum Vector ◽  
Docking Mechanism ◽  
Drug Modification ◽  
Significant Mass Effect ◽  
Significant Mass

Quasiclassical Trajectory (QCT) calculation for O(3P) + HD → OH + D and O(3P) + HD → OD + H at E col = 0.4–1.0 eV and 0.5–1.0 eV, respectively, on the lowest PES 1 3A″ of Kuppermann et al. has been done. Distribution p(ϑr) of azimuthal angles between the relative velocity k of the reactants and rotational angular momentum vector j′ of either OH or OD , p(φr) of polar as well as dihedral angles correlating k - k′ -j′, p(ϑr, φr), and PDDCS dependent upon the scattering angle ϑt of either OH , or OD between k and k′ of the reactants and products, respectively, are presented and discussed. The stereodynamics and isotopic mass effects at the smallest possible collision energies 0.4 eV and 0.5 eV for OH and OD , respectively, are significantly different. The significant mass effect with quotient 1/2 of H/D, at the corresponding collision threshold may be applied for the investigation of docking mechanism, drug modification and delivery.

Sign in / Sign up

Export Citation Format

Share Document