scholarly journals Combining Ordinary Differential Equations with Rigid Body Dynamics: Teaching a Second-year Engineering Dynamics Course to Two-year College Graduates

2016 ◽  
Author(s):  
Roes Budiman ◽  
Vishash Sharma
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Ordinary Differential Equations ◽  
College Graduates ◽  
Rigid Body Dynamics ◽  
Two Year College ◽  
Body Dynamics ◽  
Second Year

scholarly journals Equations of Motion for Train Derailment Dynamics

2007 ◽  
Author(s):  
D. Y. Jeong ◽  
M. L. Lyons ◽  
O. Orringer ◽  
A. B. Perlman
Keyword(s):  
Differential Equations ◽  
Rigid Body ◽  
Equations Of Motion ◽  
Computer Code ◽  
Relative Effect ◽  
Small Time ◽  
Rigid Body Dynamics ◽  
Train Derailment ◽  
Body Dynamics ◽  
Sensitivity Studies

This paper describes a planar or two-dimensional model to examine the gross motions of rail cars in a generalized train derailment. Three coupled, second-order differential equations are derived from Newton’s Laws to calculate rigid-body car motions with time. Car motions are defined with respect to a right-handed and fixed (i.e., non-rotating) reference frame. The rail cars are translating and rotating but not deforming. Moreover, the differential equations are considered as stiff, requiring relatively small time steps in the numerical solution, which is carried out using a FORTRAN computer code. Sensitivity studies are conducted using the purpose-built model to examine the relative effect of different factors on the derailment outcome. These factors include the number of cars in the train makeup, car mass, initial translational and rotational velocities, and coefficients of friction. Derailment outcomes include the number of derailed cars, maximum closing velocities (i.e., relative velocities between impacting cars), and peak coupler forces. Results from the purpose-built model are also compared to those from a model for derailment dynamics developed using commercial software for rigid-body dynamics called Automatic Dynamic Analysis of Mechanical Systems (ADAMS). Moreover, the purpose-built and the ADAMS models produce nearly identical results, which suggest that the dynamics are being calculated correctly in both models.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

New solutions of classical problems in rigid body dynamics

2015 ◽  
Vol 69 ◽  
pp. 40-44
Author(s):  
H.M. Yehia ◽  
E. Saleh ◽  
S.F. Megahid
Keyword(s):  
Rigid Body ◽  
Rigid Body Dynamics ◽  
Body Dynamics

scholarly journals In Silico Single-Molecule Manipulation of DNA with Rigid Body Dynamics

2014 ◽  
Vol 10 (2) ◽  
pp. e1003456 ◽  
Author(s):  
Pascal Carrivain ◽  
Maria Barbi ◽  
Jean-Marc Victor
Keyword(s):  
Rigid Body ◽  
Single Molecule ◽  
In Silico ◽  
Rigid Body Dynamics ◽  
Body Dynamics ◽  
Single Molecule Manipulation

On so‐called singular constraints in rigid‐body dynamics

1986 ◽  
Vol 54 (7) ◽  
pp. 585-586
Author(s):  
Stephen F. Felszeghy
Keyword(s):  
Rigid Body ◽  
Rigid Body Dynamics ◽  
Body Dynamics

Rigid Body Dynamics

2014 ◽  
pp. 191-227 ◽  
Author(s):  
Pål Johan From ◽  
Jan Tommy Gravdahl ◽  
Kristin Ytterstad Pettersen
Keyword(s):  
Rigid Body ◽  
Rigid Body Dynamics ◽  
Body Dynamics
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