%0 Journal Article
	%A V. Tawiwat and  T. Amornthep and  P. Pnop
	%D 2008
	%J International Journal of Mechanical and Mechatronics Engineering
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 15, 2008
	%T Analysis and Application of in Indirect MinimumJerk Method for Higher order Differential Equation in Dynamics Optimization Systems
	%U https://publications.waset.org/pdf/11285
	%V 15
	%X 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 considers the indirect minimum Jerk
method for higher order differential equation in dynamics
optimization proposes a simple yet very interesting indirect jerks
approaches in designing the time-dependent system yielding an
alternative optimal solution. Extremal solutions for the cost functions
of indirect jerks are found using the dynamic optimization methods
together with the numerical approximation. This case considers the
linear equation of a simple system, for instance, mass, spring and
damping. The simple system uses two mass connected together by
springs. The boundary initial is defined the fix end time and end
point. The higher differential order is solved by Galerkin-s methods
weight residual. As the result, the 6th higher differential order shows
the faster solving time.
	%P 285 - 289