Struve function - Revision history

99.241.166.168: finished html to {{math|...}} and improvements to Latex formulas

2014-04-01T05:49:23Z

finished html to {{math|...}} and improvements to Latex formulas

← Older revision		Revision as of 07:49, 1 April 2014
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en>Myasuda: sp

2014-03-02T04:27:15Z

← Older revision		Revision as of 06:27, 2 March 2014
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	In [[physics]] the study of rigid body motion provides for several ways of defining the acceleration state of a rigid body. The classical definition of acceleration entails following a single particle/point along the rigid body and observing its changes of [[velocity]]. In this article the notion of spatial acceleration is explored, which entails looking at a fixed (unmoving) point in space and observing the changes of [[velocity]] of whatever particle/point happens to coincide with the observation point. This is similar to the acceleration definition fluid dynamics where typically one can measure velocity and/or accelerations on a fixed locate inside a testing apparatus.		Hi there! :) My name is Marylou, I'm a student studying Biological Sciences from Bad Driburg, Germany.<br><br>my weblog :: [http://ll.my/wordpressdropboxbackup288861 wordpress backup plugin]

	~~== Definition ==~~
	Consider a moving rigid body and the velocity of a particle/point ''P'' along the body being a function of the position and velocity of a center particle/point ''C'' and the angular velocity <math>\vec \omega</math>.

	~~The linear velocity vector <math>\vec v_P</math> at ''P'' is expressed in terms of the velocity vector <math>\vec v_C</math> at ''C'' as~~:

	~~<math>\vec v_P = \vec v_C + \vec \omega \times (\vec r_P-\vec r_C~~)~~</math>~~

	~~where <math>\vec \omega</math>~~ is ~~the angular velocity vector.~~

	~~The [[Material derivative\|material acceleration]] at~~ '~~'P'' is:~~

	~~<math>\vec a_P = \frac{{\rm d} \vec v_P}{{\rm d} t}</math>~~

	~~<math>\vec a_P = \vec a_C + \vec \alpha \times (\vec r_P-\vec r_C) + \vec \omega \times (\vec v_P-\vec v_C)</math>~~

	~~where <math>\vec \alpha</math> is the angular acceleration vector.~~

	~~The spatial acceleration <math>\vec \psi_P</math> at ''P'' is expressed in terms of the spatial acceleration <math>\vec \psi_C</math> at ''C'' as:~~

	~~<math>\vec \psi_P = \frac{\partial \vec v_P}{\partial t}</math>~~

	~~<math> \vec{\psi}_{P} = \vec{\psi}_{C}+\vec{\alpha}\times(\vec{r}_{P}-\vec{r}_{C}) </math>~~

	~~which is similar to the velocity transformation above.~~

	~~In general the spatial acceleration <math>\vec \psi_P</math> of~~ a ~~particle point ''P'' that is moving with linear velocity <math>\vec v_P</math> is derived~~ from ~~the material acceleration <math>\vec a_P</math> at ''P'' as:~~

	<~~math~~> ~~\vec{\psi}_{P}=\vec{a}_{P}-\vec{\omega}\times\vec{v}_{P}~~ <~~/math~~>

	~~{{Expand section\|date=April 2012}}~~

	~~==References==~~
	*{{cite book\|title=Fluid Mechanics\|author=Frank M. White\|publisher=McGraw-Hill Professional\|year=2003\|isbn=0-07-240217-2}}.
	*{{cite book\|title=Robot Dynamics Algorithms\|author=Roy Featherstone\|publisher=Springer\|year=1987\|isbn=0-89838-230-0}}. This reference effectively combines [[screw theory]] with rigid body [[dynamics (mechanics)\|dynamics]] for robotic applications. The author also chooses to use spatial accelerations extensively in place of material accelerations as they simplify the equations and allows for compact notation.
	*JPL DARTS page has a section on spatial operator algebra (link: ~~[http://dshell.jpl.nasa.gov/SOA/index.php]) as well as an extensive list of references (link~~: [http://~~dshell~~.~~jpl.nasa.gov~~/~~References/index.php]).~~
	*{{cite book\|title=Springer Handbook of Robotics\|author=Bruno Siciliano, [[Oussama Khatib]]\|publisher=Springer\|year=2008\|isbn=}}. Page 41 (link: Google Books [http://books.google.com/books?id=Xpgi5gSuBxsC&printsec=frontcover#PPA40,M1]) defines spatial accelerations for use in rigid body mechanics.

	~~[[Category:Rigid bodies]]~~
	~~[[Category:Acceleration]~~]

en>Addbot: Bot: Migrating 4 interwiki links, now provided by Wikidata on d:q2607374

2013-03-01T06:07:33Z

Bot: Migrating 4 interwiki links, now provided by Wikidata on d:q2607374

← Older revision		Revision as of 08:07, 1 March 2013
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If a lot~~ of ~~artificial components are on the content label, it's wise to pass on~~ the ~~meгchandise.~~<br><br>~~If you are expectant or nursing yoս should remain healthy. Pregnant women oսght [http~~:~~//Howardbkraftesq.com/articles/vigrx~~-~~plus-growth-chart-get-seriously-interested-in-nourishment-follow-this-advice~~/ where ~~to buy vigrx plus In~~ the ~~uk] alաaуs be sure to consume еnough heаlthy protеins~~. Sadly, they can not need tо enjoy. Try blеnding ovum into your day smoothy for additional protein. Expectant women must loߋk into ovum for an sսperb way tο obtain proteins and ways tο have a wholesome dish with very low energy and no fat. 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You can bսild weɑk bones should you not take in adequate~~ [http://~~Escortlaradana~~.com/~~author/waveitch/ Does vigrx plus Works~~] calcium. This painful sickness causes your your bones to change delicate and fraցile.<br><br>SlumЬering ailments often meɑns that you must change your dietary program. Food items forces yоu to really feel much more notify, whilе some can help to chill out yoս. So, don't rush into mattress having a complete stomacɦ.<br><br>Aѕ you've read through, nutrition can better your lifestyle. Nutrients needs to be үour daily goal for ~~the healthier daily life~~.		In [[physics]] the study of rigid body motion provides for several ways of defining the acceleration state of a rigid body. The classical definition of acceleration entails following a single particle/point along the rigid body and observing its changes of [[velocity]]. In this article the notion of spatial acceleration is explored, which entails looking at a fixed (unmoving) point in space and observing the changes of [[velocity]] of whatever particle/point happens to coincide with the observation point. This is similar to the acceleration definition fluid dynamics where typically one can measure velocity and/or accelerations on a fixed locate inside a testing apparatus.

			== Definition ==
			Consider a moving rigid body and the velocity of a particle/point ''P'' along the body being a function of the position and velocity of a center particle/point ''C'' and the angular velocity <math>\vec \omega</math>.

			The linear velocity vector <math>\vec v_P</math> at ''P'' is expressed in terms of the velocity vector <math>\vec v_C</math> at ''C'' as:

			<math>\vec v_P = \vec v_C + \vec \omega \times (\vec r_P-\vec r_C)</math>

			where <math>\vec \omega</math> is the angular velocity vector.

			The [[Material derivative\|material acceleration]] at ''P'' is:

			<math>\vec a_P = \frac{{\rm d} \vec v_P}{{\rm d} t}</math>

			<math>\vec a_P = \vec a_C + \vec \alpha \times (\vec r_P-\vec r_C) + \vec \omega \times (\vec v_P-\vec v_C)</math>

			where <math>\vec \alpha</math> is the angular acceleration vector.

			The spatial acceleration <math>\vec \psi_P</math> at ''P'' is expressed in terms of the spatial acceleration <math>\vec \psi_C</math> at ''C'' as:

			<math>\vec \psi_P = \frac{\partial \vec v_P}{\partial t}</math>

			<math> \vec{\psi}_{P} = \vec{\psi}_{C}+\vec{\alpha}\times(\vec{r}_{P}-\vec{r}_{C}) </math>

			which is similar to the velocity transformation above.

			In general the spatial acceleration <math>\vec \psi_P</math> of a particle point ''P'' that is moving with linear velocity <math>\vec v_P</math> is derived from the material acceleration <math>\vec a_P</math> at ''P'' as:

			<math> \vec{\psi}_{P}=\vec{a}_{P}-\vec{\omega}\times\vec{v}_{P} </math>

			{{Expand section\|date=April 2012}}

			==References==
			*{{cite book\|title=Fluid Mechanics\|author=Frank M. White\|publisher=McGraw-Hill Professional\|year=2003\|isbn=0-07-240217-2}}.
			*{{cite book\|title=Robot Dynamics Algorithms\|author=Roy Featherstone\|publisher=Springer\|year=1987\|isbn=0-89838-230-0}}. This reference effectively combines [[screw theory]] with rigid body [[dynamics (mechanics)\|dynamics]] for robotic applications. The author also chooses to use spatial accelerations extensively in place of material accelerations as they simplify the equations and allows for compact notation.
			*JPL DARTS page has a section on spatial operator algebra (link: [http://dshell.jpl.nasa.gov/SOA/index.php]) as well as an extensive list of references (link: [http://dshell.jpl.nasa.gov/References/index.php]).
			*{{cite book\|title=Springer Handbook of Robotics\|author=Bruno Siciliano, [[Oussama Khatib]]\|publisher=Springer\|year=2008\|isbn=}}. Page 41 (link: Google Books [http://books.google.com/books?id=Xpgi5gSuBxsC&printsec=frontcover#PPA40,M1]) defines spatial accelerations for use in rigid body mechanics.

			[[Category:Rigid bodies]]
			[[Category:Acceleration]]

en>VolkovBot: r2.7.2) (Robot: Adding sr:Струвеове функције

2012-08-21T16:23:10Z

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