A geometric approach to establishment of datum reference frames

Author(s):  
J.B. Gou ◽  
Y.X. Chu ◽  
Z.X. Li
Author(s):  
David D. Nolte

This chapter emphasizes the importance of a geometric approach to dynamics. The central objects of interest are trajectories of a dynamical system through multidimensional spaces composed of generalized coordinates. Trajectories through configuration space are parameterized by the path length element, which becomes an important feature in later chapters on relativity and metric spaces. Trajectories through state space are defined by mathematical flow equations whose flow fields and flow lines become the chief visualization tool for complex dynamics. Coordinate transformations and Jacobian matrices are used throughout this text, and the transformation to noninertial frames introduces fictitious forces like the Coriolis force that are experienced by observers in noninertial frames. Uniformly rotating frames provide the noninertial reference frames for the description of rigid-body motion.


Author(s):  
S. Buonchristiano ◽  
C. P. Rourke ◽  
B. J. Sanderson

2001 ◽  
Author(s):  
Joseph S. Lappin ◽  
Duje Tadin ◽  
Emily Grossman

1984 ◽  
Vol 45 (C6) ◽  
pp. C6-87-C6-94
Author(s):  
H. Reinhardt ◽  
R. Balian ◽  
Y. Alhassid

1989 ◽  
Vol 17 (2) ◽  
pp. 86-99 ◽  
Author(s):  
I. Gardner ◽  
M. Theves

Abstract During a cornering maneuver by a vehicle, high forces are exerted on the tire's footprint and in the contact zone between the tire and the rim. To optimize the design of these components, a method is presented whereby the forces at the tire-rim interface and between the tire and roadway may be predicted using finite element analysis. The cornering tire is modeled quasi-statically using a nonlinear geometric approach, with a lateral force and a slip angle applied to the spindle of the wheel to simulate the cornering loads. These values were obtained experimentally from a force and moment machine. This procedure avoids the need for a costly dynamic analysis. Good agreement was obtained with experimental results for self-aligning torque, giving confidence in the results obtained in the tire footprint and at the rim. The model allows prediction of the geometry and of the pressure distributions in the footprint, since friction and slip effects in this area were considered. The model lends itself to further refinement for improved accuracy and additional applications.


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