Cite the paper
Kravets V.V., Bas K.M., Kravets T.V., Zubariev M.S. & Tokar L.A. (2016). Kinetostatics of Wheel Vehicle in the Category of Spiral-Screw Routes. Mechanics, Materials Science & Engineering, Vol 5. doi:10.13140/RG.2.1.1010.3921
Authors: Kravets V.V., Bas K.M., Kravets T.V., Zubariev M.S., Tokar L.A.
ABSTRACT. Deterministic mathematical model of kinetostatics of wheel vehicle in terms of different modes of spatial motion in the context of curved route is proposed. Earth-based coordinate system is introduced which pole and axial orientation are determined by the convenience of route description as well as vehicle-related coordinates which pole axial orientation are determined within inertial space with the help of natural trihedral. Turn of the natural trihedral within inertial coordinates is described by means of quaternion matrices in the context of Rodrigues-Hamilton parameters. Rodrigues-Hamilton parameters are in matrix form in direct accordance with specified hodograph. Kinetostatics of wheel vehicle is considered in terms of spatial motion with an allowance for three-dimensional aerodynamic forces, gravity, and tangential and centrifugal inertial forces. In the context of spiral-screw lines deterministic mathematical model of wheel vehicle kinetostatics is proposed in the form of hodograph in terms of uniform motion, accelerated motion, and decelerated motion within following route sections: straight and horizontal; in terms of vertical grade; in terms of horizontal plane. Analytical approach to determine animated contact drive-control forces of wheel vehicle for structural diagrams having one and two support points involving of a driving-driven wheel characteristic is proposed based on kinetostatics equations. Mathematical model of wheel vehicle kinetostatics in terms of spatial motion is constructed on the basis of nonlinear differential Euler-Lagrange equations; it is proposed to consider physically implemented motion trajectories of wheel vehicles in the context of spiral-screw lines; hodograph determines spatial displacement; Rodrigues-Hamilton parameters determines spatial turn; Varignon theorem is applied to identify components of drive (control) force. The obtained results make it possible to solve a wide range of problems connected with dynamic design of wheel vehicles involving controllability, and estimation of dynamic load of both system and support surface.
Keywords: dynamic design, mathematical model, Euler-Lagrange equations, kinetostatics, contact forces, spiral-screw trajectory, hodograph
 Hachaturov, A.A., Afanasiev, V.L., Vasiliev, V.S. Dynamics of “road-tire-vehicle-driver” system (in Russian). – M.: “Mashinostroenie”, 1976. – 535 P.
 Martynyuk, A.A., Lobas, L.G., Nikitina, N.V. Dynamics and sustainability of transport vehicle wheelsetmovement (in Russian). – Kiev: Tekhnika, 1981. – 223 P.
 Kravets, V.V., Kravets, T.V. Evaluation of the Centrifugal, Coriolis and Gyroscopic Forces on a Railroad Vehicle Moving at High Speed. Int. Appl. Mech. 2008. 44, No.1. P. 101-109.
 Igdalov, I.M., Kuchma, L.D., Poliakov, N.V., Sheptun, Yu.D. Rocket as a controlled object (in Russian). – Dnipropetrovsk.: ART-press. 2004. – 544 P.
 Kravets, T.V. Control forces and moments determining in the process of asymmetric aircraft along program trajectory of complex spatial configuration. Technical Mechanics. 2003. No. 1. P. 60-65.
 Beshta O., Kravets V., Bas K., Kravets T., Tokar L. Control of tandem-type two-wheel vehicle at various notion modes along spatial curved lay of line. Power Engineering, Control and Information Technologies in Geotechnical Systems, 2015 Taylor and Francis Group, London, ISBN 978-1-138-02804-3, P. 27-32. DOI: 10.1201/b18475-6
 Gerasiuta, N.F., Novikov, A.V., Beletskaia, M.G. Flight dynamics. Key tasks of dynamic design of rockets (in Russian). – Dnipropetrovsk.: M.K. Yangel State Design Office “Yuzhnoe”. 1998. – 366 P.
 Kravets V.V., Bass K.M., Kravets T.V., Tokar L.A. Dynamic Design of Ground Transport With the Help of Computation Experiment. Mechanics, Materials Science and Engineering, October 2015 – ISSN 2412-5954, MMSE Journal. Open Access www.mmse.xyz. DOI: 10.13140/RG.2.1.2466.6643
 Kravets, V., Kravets, T., Bas, K., Tokar, L. Mathematical model of a path and hodograph of surface transport // Transport problems. – 2014. – Pp. 830-841.
 Kravets, V.V., Kravets, T.V., Kharchenko, A.V. Using quaternion matrices to describe the kinematics and nonlinear dynamics of an asymmetric rigid body // Int. Appl. Mech. – 2009. – 44. #2. – Pp. 223-232. DOI 10.1007/s10778-009-0171-1
 Lobas, L.G., Lyudm G. Theoretical mechanics (in Russian). Kiev: DETUT, 2009. 407 P.
 Kravets T.V. On the use of quaternion matrices in the analytical and computational solid mechanics. Technical Mechanics.2013. Issue 3: 91-102 P.
Mechanics, Materials Science & Engineering Journal by Magnolithe GmbH is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at www.mmse.xyz.