Analytical Prediction - Revision history

Richard.Udall at 16:12, 9 July 2019

2019-07-09T16:12:02Z

← Older revision		Revision as of 12:12, 9 July 2019
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	'''Claimed/Edited by Lauren Widjaja (Fall 2018)'''		'''Claimed/Edited by Lauren Widjaja (Fall 2018)'''

	'''Deprecated by Richard Udall (Summer 2019), see [[Kinematics]] instead'''		'''Deprecated by Richard Udall (Summer 2019), see [[Kinematics]] instead, some content may be spliced from here into that article'''

	Using the momentum principle and a knowledge of the net force on an object, we can iterative calculations to predict the motion of that object over time. We have already seen how to do this with a constant net force, and will soon see how to do it with a varying force. However, if the force is constant, we may also solve the problem analytically, with no iteration necessary. Many non-constant forces may also be solved analytically, but this requires more complex mathematics.		Using the momentum principle and a knowledge of the net force on an object, we can iterative calculations to predict the motion of that object over time. We have already seen how to do this with a constant net force, and will soon see how to do it with a varying force. However, if the force is constant, we may also solve the problem analytically, with no iteration necessary. Many non-constant forces may also be solved analytically, but this requires more complex mathematics.

Richard.Udall: Undo revision 35721 by Richard.Udall (talk)

2019-07-09T16:11:10Z

Undo revision 35721 by Richard.Udall (talk)

← Older revision		Revision as of 12:11, 9 July 2019
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	'''Claimed/Edited by Lauren Widjaja (Fall 2018)'''		'''Claimed/Edited by Lauren Widjaja (Fall 2018)'''

	'''Deprecated by Richard Udall (Summer 2019), see [[Kinematics]] instead~~, some content may be spliced from here into that article~~'''		'''Deprecated by Richard Udall (Summer 2019), see [[Kinematics]] instead'''

	Using the momentum principle and a knowledge of the net force on an object, we can iterative calculations to predict the motion of that object over time. We have already seen how to do this with a constant net force, and will soon see how to do it with a varying force. However, if the force is constant, we may also solve the problem analytically, with no iteration necessary. Many non-constant forces may also be solved analytically, but this requires more complex mathematics.		Using the momentum principle and a knowledge of the net force on an object, we can iterative calculations to predict the motion of that object over time. We have already seen how to do this with a constant net force, and will soon see how to do it with a varying force. However, if the force is constant, we may also solve the problem analytically, with no iteration necessary. Many non-constant forces may also be solved analytically, but this requires more complex mathematics.

Richard.Udall at 16:10, 9 July 2019

2019-07-09T16:10:11Z

← Older revision		Revision as of 12:10, 9 July 2019
Line 3:		Line 3:
	'''Claimed/Edited by Lauren Widjaja (Fall 2018)'''		'''Claimed/Edited by Lauren Widjaja (Fall 2018)'''

	'''Deprecated by Richard Udall (Summer 2019), see [[Kinematics]] instead'''		'''Deprecated by Richard Udall (Summer 2019), see [[Kinematics]] instead, some content may be spliced from here into that article'''

	Using the momentum principle and a knowledge of the net force on an object, we can iterative calculations to predict the motion of that object over time. We have already seen how to do this with a constant net force, and will soon see how to do it with a varying force. However, if the force is constant, we may also solve the problem analytically, with no iteration necessary. Many non-constant forces may also be solved analytically, but this requires more complex mathematics.		Using the momentum principle and a knowledge of the net force on an object, we can iterative calculations to predict the motion of that object over time. We have already seen how to do this with a constant net force, and will soon see how to do it with a varying force. However, if the force is constant, we may also solve the problem analytically, with no iteration necessary. Many non-constant forces may also be solved analytically, but this requires more complex mathematics.

Richard.Udall at 16:09, 9 July 2019

2019-07-09T16:09:42Z

← Older revision		Revision as of 12:09, 9 July 2019
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	'''Claimed/Edited by Lauren Widjaja (Fall 2018)'''		'''Claimed/Edited by Lauren Widjaja (Fall 2018)'''

	'''~~Edited~~ by Richard Udall (Summer 2019)'''		'''Deprecated by Richard Udall (Summer 2019), see [[Kinematics]] instead'''

	Using the momentum principle and a knowledge of the net force on an object, we can iterative calculations to predict the motion of that object over time. We have already seen how to do this with a constant net force, and will soon see how to do it with a varying force. However, if the force is constant, we may also solve the problem analytically, with no iteration necessary. Many non-constant forces may also be solved analytically, but this requires more complex mathematics.		Using the momentum principle and a knowledge of the net force on an object, we can iterative calculations to predict the motion of that object over time. We have already seen how to do this with a constant net force, and will soon see how to do it with a varying force. However, if the force is constant, we may also solve the problem analytically, with no iteration necessary. Many non-constant forces may also be solved analytically, but this requires more complex mathematics.

Richard.Udall: /* A Mathematical Model */

2019-07-09T16:08:54Z

A Mathematical Model

← Older revision		Revision as of 12:08, 9 July 2019
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	Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.		Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

	~~[[File: 1.jpg\|150px]]~~

	Here, X bar is the arithmetic mean, sigma f x is the sum of all the values, and sigma f is the total number of terms. Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.		Here, X bar is the arithmetic mean, sigma f x is the sum of all the values, and sigma f is the total number of terms. Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

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	y(t) = 1/2(-g)t^2 + (vy, o)t + yo		y(t) = 1/2(-g)t^2 + (vy, o)t + yo



	===A Computational Model===		===A Computational Model===

Richard.Udall at 16:05, 9 July 2019

2019-07-09T16:05:15Z

← Older revision		Revision as of 12:05, 9 July 2019
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	By Hayden McLeod (hmcleod6)		By Hayden McLeod (hmcleod6)

	'''Claimed/Edited by Lauren Widjaja (Fall 2018)'''		'''Claimed/Edited by Lauren Widjaja (Fall 2018)'''

	Using the ~~Momentum~~ principle, we can ~~use~~ net force to ~~predict momentum over~~ a ~~period of time~~. However, if the force is constant, ~~this simplifies a lot of~~ the ~~steps because there is~~ no ~~need to do it iteratively although it is possible to still use the Momentum Principle. This however will require more steps~~. ~~Instead, since force is~~ constant, ~~a lot of quantities can be found using a linear model by using a set of equations to solve for different values~~.		'''Edited by Richard Udall (Summer 2019)'''

			Using the momentum principle and a knowledge of the net force on an object, we can iterative calculations to predict the motion of that object over time. We have already seen how to do this with a constant net force, and will soon see how to do it with a varying force. However, if the force is constant, we may also solve the problem analytically, with no iteration necessary. Many non-constant forces may also be solved analytically, but this requires more complex mathematics.

	==The Main Idea==		==The Main Idea==

	~~Analytical~~ prediction ~~uses a mathematical function that can describe~~ the ~~position or velocity~~ of a ~~system at any given~~ time. In contrast to iterative prediction, ~~this means that~~ there is no need to ~~make multiple~~ calculations at ~~small steps in order to find a solution~~. However~~, due to the method of derivation of the velocity~~, the ~~analytical method is~~ only ~~accurate to a high degree when~~ the force ~~applied to the system~~ is constant. Due to this limitation, ~~the~~ iterative prediction ~~method is much more generally applicable~~. However, ~~it is~~ used ~~to simplify models with complicated steps to get~~ a ~~good estimate~~ of the ~~data. The analytical prediction is also a useful way to determine values~~ in ~~a projectile motion situation~~.		Analytic prediction is the process of producing a general formula for an objects motion over time. In contrast to iterative prediction, there is no need to perform calculations at regular intervals. However, the assumptions we will be making here only hold if the force is constant: non-constant forces demand the use of differential equations as a method of solution in all but the simplest cases. Due to this limitation, iterative prediction may be applied directly in a wider variety of situations, and may be used in cases where the forces are too complex to allow any analytic solution (see [[Determinism]]). However, analytic prediction may be used for many simpler cases, and in more complex cases may allow for estimation of values if a computer program is unavailable or prohibitively slow. One of the most prominent examples of the use of analytic modelling will be in solving [[Projectile Motion]] problems.

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

Lwidjaja3: /* The Main Idea */

2018-11-26T04:24:37Z

The Main Idea

← Older revision		Revision as of 00:24, 26 November 2018
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	==The Main Idea==		==The Main Idea==

	Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable. However, it is used to simplify models with complicated steps to get a good estimate of the data.		Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable. However, it is used to simplify models with complicated steps to get a good estimate of the data. The analytical prediction is also a useful way to determine values in a projectile motion situation.

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

Lwidjaja3 at 04:23, 26 November 2018

2018-11-26T04:23:16Z

← Older revision		Revision as of 00:23, 26 November 2018
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	This average velocity can be used to determine the change in position as an application to this problem. This will be shown in the next example.		This average velocity can be used to determine the change in position as an application to this problem. This will be shown in the next example.

	===~~Moderate~~===		===Middling===
	A car is traveling at a speed of (18, -2, 0) m/s. Later, the car is observed to be going (22, 6, 0) m/s. If the car started at the location (40, 170, 0) what is it's position after 30 seconds?		A car is traveling at a speed of (18, -2, 0) m/s. Later, the car is observed to be going (22, 6, 0) m/s. If the car started at the location (40, 170, 0) what is it's position after 30 seconds?

Lwidjaja3 at 04:20, 26 November 2018

2018-11-26T04:20:33Z

← Older revision		Revision as of 00:20, 26 November 2018
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	'''Claimed/Edited by Lauren Widjaja (Fall 2018)'''		'''Claimed/Edited by Lauren Widjaja (Fall 2018)'''

	Using the Momentum principle, we can use net force to predict momentum over a period of time. However, if the force is constant, this simplifies a lot of the steps because there is no need to do it iteratively. Instead, since force is constant, a lot of quantities can be found using a linear model.		Using the Momentum principle, we can use net force to predict momentum over a period of time. However, if the force is constant, this simplifies a lot of the steps because there is no need to do it iteratively although it is possible to still use the Momentum Principle. This however will require more steps. Instead, since force is constant, a lot of quantities can be found using a linear model by using a set of equations to solve for different values.
	==The Main Idea==		==The Main Idea==

Lwidjaja3: /* Middling */

2018-11-26T04:13:33Z

Middling

← Older revision		Revision as of 00:13, 26 November 2018
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	This average velocity can be used to determine the change in position as an application to this problem. This will be shown in the next example.		This average velocity can be used to determine the change in position as an application to this problem. This will be shown in the next example.

	===~~Middling~~===		===Moderate===
	A car is traveling at a speed of (18, -2, 0) m/s. Later, the car is observed to be going (22, 6, 0) m/s. If the car started at the location (40, 170, 0) what is it's position after 30 seconds?		A car is traveling at a speed of (18, -2, 0) m/s. Later, the car is observed to be going (22, 6, 0) m/s. If the car started at the location (40, 170, 0) what is it's position after 30 seconds?