Predicting Change in multiple dimensions - Revision history

Richard.Udall at 18:24, 29 July 2019

2019-07-29T18:24:40Z

← Older revision		Revision as of 14:24, 29 July 2019
Line 1:		Line 1:
	'''Claimed by rbose7 Fall 2015'''		'''Claimed by rbose7 Fall 2015'''

			'''Edited by Richard Udall Summer 2019'''

	Here we analyze how to apply the same iterative methods we have hitherto used in one dimension to predict motion in multiple dimensions. In essence the situation may be broken down into three one dimensional problems, but when we are dealing with varying forces, it is necessary to generalize the probability that motion in one dimension will alter the forces in another dimension.		Here we analyze how to apply the same iterative methods we have hitherto used in one dimension to predict motion in multiple dimensions. In essence the situation may be broken down into three one dimensional problems, but when we are dealing with varying forces, it is necessary to generalize the probability that motion in one dimension will alter the forces in another dimension.

Richard.Udall: /* History */

2019-07-29T18:24:08Z

History

← Older revision		Revision as of 14:24, 29 July 2019
Line 193:		Line 193:
	==History==		==History==

	The first school of thought in dynamics was the Aristotelian school, which was completely incorrect, in that it claimed that motion had to be continuously sustained by a force being imparted, leading to claims such as an arrow being driven by the air.<ref> https://plato.stanford.edu/entries/aristotle-metaphysics/ </ref> The first to move away from this was John Philoponus, who proposed the idea of impetus, which held that objects were imparted with some essence of motion, which is then depleted over the course of the objects motion. This is substantially closer to reality, but still not accurate. Galileo noted from experiment the existence of inertia, and the separability of dimensions. <ref> http://ffden-2.phys.uaf.edu/211.fall2000.web.projects/J.%20Gentry%20and%20D.%20Arnold/phys211.html </ref> Descartes stated what we now view as momentum more explicitly, constructing it based on the principles of Cartesian metaphysics <ref> https://plato.stanford.edu/entries/descartes-physics/#StraCartPhys </ref>, and in doing so critiqued Galileo's experimentalism (although the balance between theory and experiment is still a matter of discussion today, modern physics is constructed primarily with Galileo's experimental method rather than Descartes' metaphysical justifications). As with the corresponding developments in mathematics (in which Descartes' coordinate geometry laid the basis for calculus), momentum as a concept, and the methods of analyzing motion, were developed in greater detail by Newton in ~~his~~ Principia. <ref> http://galileoandeinstein.physics.virginia.edu/lectures/momentum.html </ref>		The first school of thought in dynamics was the Aristotelian school, which was completely incorrect, in that it claimed that motion had to be continuously sustained by a force being imparted, leading to claims such as an arrow being driven by the air.<ref> https://plato.stanford.edu/entries/aristotle-metaphysics/ </ref> The first to move away from this was John Philoponus, who proposed the idea of impetus, which held that objects were imparted with some essence of motion, which is then depleted over the course of the objects motion. This is substantially closer to reality, but still not accurate. Galileo noted from experiment the existence of inertia, and the separability of dimensions. <ref> http://ffden-2.phys.uaf.edu/211.fall2000.web.projects/J.%20Gentry%20and%20D.%20Arnold/phys211.html </ref> Descartes stated what we now view as momentum more explicitly, constructing it based on the principles of Cartesian metaphysics <ref> https://plato.stanford.edu/entries/descartes-physics/#StraCartPhys </ref>, and in doing so critiqued Galileo's experimentalism (although the balance between theory and experiment is still a matter of discussion today, modern physics is constructed primarily with Galileo's experimental method rather than Descartes' metaphysical justifications). As with the corresponding developments in mathematics (in which Descartes' coordinate geometry laid the basis for calculus), momentum as a concept, and the methods of analyzing motion, were developed in greater detail by Newton in the ''Principia Mathematica''. <ref> http://galileoandeinstein.physics.virginia.edu/lectures/momentum.html </ref>

	== See also ==		== See also ==

Richard.Udall: /* See also */

2019-07-25T21:33:54Z

Richard.Udall: /* History */

2019-07-25T21:33:11Z

History

← Older revision		Revision as of 17:33, 25 July 2019
Line 193:		Line 193:
	==History==		==History==

	The first school of thought in dynamics was the Aristotelian school, which was completely incorrect, in that it claimed that motion had to be continuously sustained by a force being imparted, leading to claims such as an arrow being driven by the air.<ref> https://plato.stanford.edu/entries/aristotle-metaphysics/ </ref> The first to move away from this was John Philoponus, who proposed the idea of impetus, which held that objects were imparted with some essence of motion, which is then depleted over the course of the objects motion. This is substantially closer to reality, but still not accurate. Galileo noted from experiment the existence of inertia, and the separability of dimensions. <ref> http://ffden-2.phys.uaf.edu/211.fall2000.web.projects/J.%20Gentry%20and%20D.%20Arnold/phys211.html </ref> Descartes stated what we now view as momentum more explicitly, constructing it based on the principles of Cartesian metaphysics <ref> https://plato.stanford.edu/entries/descartes-physics/#StraCartPhys </ref>, and in doing so critiqued Galileo's experimentalism (although the balance between theory and experiment is still a matter of discussion today, modern physics is constructed primarily with Galileo's experimental method rather than Descartes' metaphysical justifications). As with the corresponding developments in mathematics (in which Descartes' coordinate geometry laid the basis for calculus), momentum as a concept, and the methods of analyzing motion, were developed in greater detail by Newton in his Principia <ref> http://galileoandeinstein.physics.virginia.edu/lectures/momentum.html </ref>		The first school of thought in dynamics was the Aristotelian school, which was completely incorrect, in that it claimed that motion had to be continuously sustained by a force being imparted, leading to claims such as an arrow being driven by the air.<ref> https://plato.stanford.edu/entries/aristotle-metaphysics/ </ref> The first to move away from this was John Philoponus, who proposed the idea of impetus, which held that objects were imparted with some essence of motion, which is then depleted over the course of the objects motion. This is substantially closer to reality, but still not accurate. Galileo noted from experiment the existence of inertia, and the separability of dimensions. <ref> http://ffden-2.phys.uaf.edu/211.fall2000.web.projects/J.%20Gentry%20and%20D.%20Arnold/phys211.html </ref> Descartes stated what we now view as momentum more explicitly, constructing it based on the principles of Cartesian metaphysics <ref> https://plato.stanford.edu/entries/descartes-physics/#StraCartPhys </ref>, and in doing so critiqued Galileo's experimentalism (although the balance between theory and experiment is still a matter of discussion today, modern physics is constructed primarily with Galileo's experimental method rather than Descartes' metaphysical justifications). As with the corresponding developments in mathematics (in which Descartes' coordinate geometry laid the basis for calculus), momentum as a concept, and the methods of analyzing motion, were developed in greater detail by Newton in his Principia. <ref> http://galileoandeinstein.physics.virginia.edu/lectures/momentum.html </ref>

	== See also ==		== See also ==

Richard.Udall: /* History */

2019-07-25T21:33:00Z

History

← Older revision		Revision as of 17:33, 25 July 2019
Line 193:		Line 193:
	==History==		==History==

	~~Before Newton~~, ~~French scientist and philosopher Descartes introduced~~ the ~~concept of momentum~~. ~~He used~~ the ~~concept~~ of ~~momentum to describe how people moved when~~ objects were ~~thrown at them~~. ~~He focused generally on~~ the ~~conservation~~ of momentum ~~when dealing with collisions. Newton's laws further expanded~~ on the ~~idea~~ of ~~conservation of momentum. The ideas that~~ <~~math~~>~~F = ma~~</~~math~~> and the ~~idea that for every action there~~ is ~~an equal and opposite reaction are~~ the basis for ~~many problems~~ and ~~concepts explained~~ in ~~this section. More information here:~~		The first school of thought in dynamics was the Aristotelian school, which was completely incorrect, in that it claimed that motion had to be continuously sustained by a force being imparted, leading to claims such as an arrow being driven by the air.<ref> https://plato.stanford.edu/entries/aristotle-metaphysics/ </ref> The first to move away from this was John Philoponus, who proposed the idea of impetus, which held that objects were imparted with some essence of motion, which is then depleted over the course of the objects motion. This is substantially closer to reality, but still not accurate. Galileo noted from experiment the existence of inertia, and the separability of dimensions. <ref> http://ffden-2.phys.uaf.edu/211.fall2000.web.projects/J.%20Gentry%20and%20D.%20Arnold/phys211.html </ref> Descartes stated what we now view as momentum more explicitly, constructing it based on the principles of Cartesian metaphysics <ref> https://plato.stanford.edu/entries/descartes-physics/#StraCartPhys </ref>, and in doing so critiqued Galileo's experimentalism (although the balance between theory and experiment is still a matter of discussion today, modern physics is constructed primarily with Galileo's experimental method rather than Descartes' metaphysical justifications). As with the corresponding developments in mathematics (in which Descartes' coordinate geometry laid the basis for calculus), momentum as a concept, and the methods of analyzing motion, were developed in greater detail by Newton in his Principia <ref> http://galileoandeinstein.physics.virginia.edu/lectures/momentum.html </ref>

	http://galileoandeinstein.physics.virginia.edu/lectures/momentum.html

	~~https:~~/~~/en.wikipedia.org/wiki/Momentum#History_of_the_concept~~

	== See also ==		== See also ==

Richard.Udall: /* References */

2019-07-25T20:55:45Z

References

← Older revision		Revision as of 16:55, 25 July 2019
Line 215:		Line 215:

	==References==		==References==
			<references/>
	~~https:~~/~~/en.wikipedia.org/wiki/Momentum~~

	~~https://en.wikibooks.org/wiki/General_Mechanics/Momentum~~

	~~http://galileoandeinstein.physics.virginia.edu/lectures/momentum.html~~

	[[Category:Momentum]]		[[Category:Momentum]]

Richard.Udall: /* The Main Idea */

2019-07-25T20:55:08Z

The Main Idea

← Older revision		Revision as of 16:55, 25 July 2019
Line 4:		Line 4:

	==The Main Idea==		==The Main Idea==
	Just as in one dimension, the linear (also known as translational) motion of an object is the vector quantity equal to the product of the mass and velocity of an object. Unlike in one dimension, we must now consider the vectors components in each direction (see [[3-Dimensional Position and Motion]] for more detail). By utilizing Newton's second law in each dimension, it is possible to predict the motion of the object in each dimension, making use of the same modelling techniques we have applied before.		Just as in one dimension, the linear (also known as translational) motion of an object is the vector quantity equal to the product of the mass and velocity of an object. Unlike in one dimension, we must now consider the vectors components in each direction (see [[3-Dimensional Position and Motion]] for more detail). By utilizing Newton's second law in each dimension, it is possible to predict the motion of the object in each dimension, making use of the same modelling techniques we have applied before.<ref> http://www.feynmanlectures.caltech.edu/I_09.html </ref>

	===A Mathematical Model===		===A Mathematical Model===

Richard.Udall: /* External Links */

2019-07-25T20:54:40Z

External Links

← Older revision		Revision as of 16:54, 25 July 2019
Line 208:		Line 208:

	===External Links===		===External Links===
			*[http://www.feynmanlectures.caltech.edu/I_09.html Feynman Lectures Chapter on Newtonian Dynamics]
	*[https://en.wikipedia.org/wiki/Momentum Wikipedia Article on Momentum]		*[https://en.wikipedia.org/wiki/Momentum Wikipedia Article on Momentum]
	*[http://hyperphysics.phy-astr.gsu.edu/hbase/mom.html Hyperphysics on Momentum]		*[http://hyperphysics.phy-astr.gsu.edu/hbase/mom.html Hyperphysics on Momentum]

Richard.Udall: /* External Links */

2019-07-25T20:52:54Z

External Links

← Older revision		Revision as of 16:52, 25 July 2019
Line 208:		Line 208:

	===External Links===		===External Links===
	*[https://en.~~wikibooks~~.org/wiki~~/General_Mechanics~~/Momentum ~~Wikibook~~ Article on Momentum]		*[https://en.wikipedia.org/wiki/Momentum Wikipedia Article on Momentum]
	*[http://hyperphysics.phy-astr.gsu.edu/hbase/mom.html Hyperphysics on Momentum]		*[http://hyperphysics.phy-astr.gsu.edu/hbase/mom.html Hyperphysics on Momentum]
	*[http://galileoandeinstein.physics.virginia.edu/lectures/momentum.html Galileo Institute on Momentum]		*[http://galileoandeinstein.physics.virginia.edu/lectures/momentum.html Galileo Institute on Momentum]

Richard.Udall: /* Connectedness */

2019-07-25T20:50:42Z

Connectedness

← Older revision		Revision as of 16:50, 25 July 2019
Line 188:		Line 188:
	==Connectedness==		==Connectedness==
	[This should be extended by a student following the [[Template]]]		[This should be extended by a student following the [[Template]]]

	For my major, computer science, there are a few applications. For example, every computational model in the section above is coded using Python. A big part of computer science is modeling real life examples on a computer to mimic situations that would be otherwise impractical or impossible to set up. For example, the model we created of the electron and proton moving would take several expensive instruments to set up and visualize the two particles. For several other instances, using the principle of momentum and analyzing the change in momentum we can model several situations using coding that would otherwise not be possible.		For my major, computer science, there are a few applications. For example, every computational model in the section above is coded using Python. A big part of computer science is modeling real life examples on a computer to mimic situations that would be otherwise impractical or impossible to set up. For example, the model we created of the electron and proton moving would take several expensive instruments to set up and visualize the two particles. For several other instances, using the principle of momentum and analyzing the change in momentum we can model several situations using coding that would otherwise not be possible.

← Older revision		Revision as of 17:33, 25 July 2019
Line 209:		Line 209:
	*[http://galileoandeinstein.physics.virginia.edu/lectures/momentum.html Galileo Institute on Momentum]		*[http://galileoandeinstein.physics.virginia.edu/lectures/momentum.html Galileo Institute on Momentum]
	*[https://phet.colorado.edu/en/simulation/legacy/projectile-motion Projectile Motion by PhET]		*[https://phet.colorado.edu/en/simulation/legacy/projectile-motion Projectile Motion by PhET]

			===Further Reading===

			*Matter and Interactions, 4th Edition

	==References==		==References==