scholarly journals Effects of mass variation on form invariance and conserved quantity of mechanical systems

2005 ◽  
Vol 54 (6) ◽  
pp. 2478
Author(s):  
Ge Wei-Kuan
Keyword(s):  
Mechanical Systems ◽  
Conserved Quantity ◽  
Mass Variation ◽  
Form Invariance

Three-order form invariance and conserved quantity

2006 ◽  
Vol 15 (8) ◽  
pp. 1672-1677 ◽  
Author(s):  
Yang Xue-Hui ◽  
Ma Shan-Jun
Keyword(s):  
Conserved Quantity ◽  
Form Invariance ◽  
Order Form

Damping-Induced Self Recovery Phenomenon in Mechanical Systems With an Unactuated Cyclic Variable

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
Dong Eui Chang ◽  
Soo Jeon
Keyword(s):  
Inverted Pendulum ◽  
Mechanical Systems ◽  
Conserved Quantity ◽  
The Self ◽  
Underactuated Mechanical Systems ◽  
Damping Force ◽  
Momentum Map ◽  
Time Integral ◽  
Conservation Of Momentum ◽  
Globally Attractive

Conservation of momentum is often used in controlling underactuated mechanical systems with symmetry. If a symmetry-breaking force is applied to the system, then the momentum is not conserved any longer in general. However, there exist forces linear in velocity such as the damping force that break the symmetry but induce a new conserved quantity in place of the original momentum map. This paper formalizes a new conserved quantity which can be constructed by combining the time integral of a general damping force and the original momentum map associated with the symmetry. From the perspective of stability theories, the new conserved quantity implies the corresponding variable possesses the self recovery phenomenon, i.e., it will be globally attractive to the initial condition of the variable. We discover that what is fundamental in the damping-induced self recovery is not the positivity of the damping coefficient but certain properties of the time integral of the damping force. The self recovery effect and theoretical findings are demonstrated by simulation results using the two-link planar manipulator and the torque-controlled inverted pendulum on a passive cart. The results in this paper will be useful in designing and controlling mechanical systems with underactuation.

Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems

2009 ◽  
Vol 18 (11) ◽  
pp. 4650-4656 ◽  
Author(s):  
Zhang Ming-Jiang ◽  
Fang Jian-Hui ◽  
Lu Kai ◽  
Zhang Ke-Jun ◽  
Li Yan
Keyword(s):  
Conformal Invariance ◽  
Mechanical Systems ◽  
Conserved Quantity ◽  
Lagrange Equations ◽  
Third Order
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