@article{(Open Science Index):https://publications.waset.org/pdf/12200,
	  title     = {Comparison between Minimum Direct and Indirect Jerks of Linear Dynamic Systems},
	  author    = {Tawiwat Veeraklaew and  Nathasit Phathana-im and  Songkit Heama},
	  country	= {},
	  institution	= {},
	  abstract     = {Both the minimum energy consumption and
smoothness, which is quantified as a function of jerk, are generally
needed in many dynamic systems such as the automobile and the
pick-and-place robot manipulator that handles fragile equipments.
Nevertheless, many researchers come up with either solely
concerning on the minimum energy consumption or minimum jerk
trajectory. This research paper proposes a simple yet very interesting
relationship between the minimum direct and indirect jerks
approaches in designing the time-dependent system yielding an
alternative optimal solution. Extremal solutions for the cost functions
of direct and indirect jerks are found using the dynamic optimization
methods together with the numerical approximation. This is to allow
us to simulate and compare visually and statistically the time history
of control inputs employed by minimum direct and indirect jerk
designs. By considering minimum indirect jerk problem, the
numerical solution becomes much easier and yields to the similar
results as minimum direct jerk problem.},
	    journal   = {International Journal of Mechanical and Mechatronics Engineering},
	  volume    = {2},
	  number    = {1},
	  year      = {2008},
	  pages     = {2 - 6},
	  ee        = {https://publications.waset.org/pdf/12200},
	  url   	= {https://publications.waset.org/vol/13},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 13, 2008},