Group 3 - Revision history

Cjcrowley at 13:59, 12 January 2012

2012-01-12T13:59:50Z

← Older revision		Revision as of 09:59, 12 January 2012
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	''Group members: Nitin Arora, Phillip Gray, Chris Rodesney, Jacob Yunis''		''Group members: Nitin Arora, Phillip Gray, Chris Rodesney, Jacob Yunis''

			[[Media: NLD_Presentation_Official_Final_Final_For_Real.pdf \| Presentation]]. '''Papers:''' [[Media: Arora_Nitin_Paper_nitin.pdf \| Nitin]], [[Media: Gray_Phillip.pdf \| Phillip]], [[Media: Yunis_Jacob_6268_final.pdf \| Jacob]], [[Media: Rodesneyinelastic_ball.pdf \| Chris]]

	[[File:sample1.jpg\| thumb \| 400px \| Typical position of the ball (blue) and plate (black) versus time for c=3.]]		[[File:sample1.jpg\| thumb \| 400px \| Typical position of the ball (blue) and plate (black) versus time for c=3.]]

Cjcrowley at 16:14, 11 January 2012

2012-01-11T16:14:26Z

← Older revision		Revision as of 12:14, 11 January 2012
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			'''Inelastic bouncing ball'''

	''Group members: Nitin Arora, Phillip Gray, Chris Rodesney, Jacob Yunis''		''Group members: Nitin Arora, Phillip Gray, Chris Rodesney, Jacob Yunis''

Cjcrowley: Protected "Group 3" ([edit=sysop] (indefinite) [move=sysop] (indefinite))

2012-01-09T16:51:28Z

Protected "Group 3" ([edit=sysop] (indefinite) [move=sysop] (indefinite))

← Older revision	Revision as of 12:51, 9 January 2012
(No difference)

Group3 at 00:01, 17 December 2011

2011-12-17T00:01:09Z

← Older revision		Revision as of 20:01, 16 December 2011
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	==Video==		==Video==
	<videoflash>aTdB7jeKulM</videoflash>		<videoflash>aTdB7jeKulM</videoflash>
			<videoflash>IfaxwbqfPSU</videoflash>

	== Results ==		== Results ==

Group3 at 23:57, 16 December 2011

2011-12-16T23:57:32Z

← Older revision		Revision as of 19:57, 16 December 2011
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	LabView was used to control the vibrating plate. LabView output the driving signal oscillating between -2.5 and 2.5 V. The signal was then passed through an amplifier whose gain was adjusted such that the minimum and maximum accelerations desired could be achieved. Data was taken by continuously increasing the amplitude of the voltage applied to the shaker table such that the acceleration slowly increased from 0g to 8g. Physically, this adjusted $\Gamma$ by increasing the amplitude of vibration while maintaining a constant frequency. This was done in steps where a constant maximum amplitude was held for a specified number of cycles. The number of cycles was control by the user. Each period of constant amplitude vibration represents a slice of the bifurcation diagram. The data from each set of constant amplitude readings was analysed independently to find the time of flight in each region then assembled into the bifurcation diagram. It is advantageous to hold the acceleration constant for longer periods of time, more cycles, so that transients can die out and more data is available. However, this results in very long experiment durations and large data files that are difficult to handle. The number of cycles held at each amplitude was varied from 5 to 60. Figure 7 shows regions of constant amplitude oscillation increasing in steps		LabView was used to control the vibrating plate. LabView output the driving signal oscillating between -2.5 and 2.5 V. The signal was then passed through an amplifier whose gain was adjusted such that the minimum and maximum accelerations desired could be achieved. Data was taken by continuously increasing the amplitude of the voltage applied to the shaker table such that the acceleration slowly increased from 0g to 8g. Physically, this adjusted $\Gamma$ by increasing the amplitude of vibration while maintaining a constant frequency. This was done in steps where a constant maximum amplitude was held for a specified number of cycles. The number of cycles was control by the user. Each period of constant amplitude vibration represents a slice of the bifurcation diagram. The data from each set of constant amplitude readings was analysed independently to find the time of flight in each region then assembled into the bifurcation diagram. It is advantageous to hold the acceleration constant for longer periods of time, more cycles, so that transients can die out and more data is available. However, this results in very long experiment durations and large data files that are difficult to handle. The number of cycles held at each amplitude was varied from 5 to 60. Figure 7 shows regions of constant amplitude oscillation increasing in steps

	[[File: steps.JPG \| ~~400px~~ \| thumb \| ~~right~~ \| Steps of constant amplitude vibrations ]]		[[File: steps.JPG \| 350px \| thumb \| left \| Steps of constant amplitude vibrations ]]

	The data was analysed by looking at each group of constant amplitude vibrations independently. The time of flight was measured for each bounce and the initial 10 bounces were ignored. This allows for transients to die out. It is not necessary to eliminate many cycles because once the ball reaches a sticking region all the previous bounces are forgotten.		The data was analysed by looking at each group of constant amplitude vibrations independently. The time of flight was measured for each bounce and the initial 10 bounces were ignored. This allows for transients to die out. It is not necessary to eliminate many cycles because once the ball reaches a sticking region all the previous bounces are forgotten.

			==Video==
			<videoflash>aTdB7jeKulM</videoflash>

	== Results ==		== Results ==

Group3 at 17:03, 16 December 2011

2011-12-16T17:03:41Z

← Older revision		Revision as of 13:03, 16 December 2011
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	<gallery widths="250px" heights="200px" perrow="3">		<gallery widths="250px" heights="200px" perrow="3">
	Image:singlebouncemode.jpg\| <math>c=1</math>		Image:singlebouncemode.jpg\| <math>gamma=1.75</math>
	Image:twobouncemode.jpg\| <math>c=2</math>		Image:twobouncemode.jpg\| <math>gamma=2.25</math>
	Image:bimodalmode.jpg\| <math>c=3</math>		Image:bimodalmode.jpg\| <math>gamma=3.5</math>
	</gallery>		</gallery>

Group3 at 17:02, 16 December 2011

2011-12-16T17:02:54Z

← Older revision		Revision as of 13:02, 16 December 2011
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	In the higher acceleration regions of the bifurcation diagrams we see that things become more chaotic. To look for more patterns in the data that may not be visible in the bifurcation diagram, return maps were generated to visualize the relationship between the time of flight for the current bounce and the one preceding it. Return maps for $\Gamma$ of 1.75, 2.25, and 3.5g are shown in Figures 9, 10 and 11.		In the higher acceleration regions of the bifurcation diagrams we see that things become more chaotic. To look for more patterns in the data that may not be visible in the bifurcation diagram, return maps were generated to visualize the relationship between the time of flight for the current bounce and the one preceding it. Return maps for $\Gamma$ of 1.75, 2.25, and 3.5g are shown in Figures 9, 10 and 11.

	~~[[File: singlebouncemode.JPG \| 400px \| thumb \| left \| Return Map of Gamma = 1.75 ]]~~
	~~[[File: twobouncemode.JPG \| 400px \| thumb \| center \| Return Map of Gamma = 2.25 ]]~~
	~~[[File: bimodalmode.JPG \| 400px \| thumb \| right \| Return Map of Gamma = 3.75 ]]~~

	<gallery widths="250px" heights="200px" perrow="3">		<gallery widths="250px" heights="200px" perrow="3">

Group3 at 17:02, 16 December 2011

2011-12-16T17:02:25Z

← Older revision		Revision as of 13:02, 16 December 2011
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	[[File: bimodalmode.JPG \| 400px \| thumb \| right \| Return Map of Gamma = 3.75 ]]		[[File: bimodalmode.JPG \| 400px \| thumb \| right \| Return Map of Gamma = 3.75 ]]

			<gallery widths="250px" heights="200px" perrow="3">
			Image:singlebouncemode.jpg\| <math>c=1</math>
			Image:twobouncemode.jpg\| <math>c=2</math>
			Image:bimodalmode.jpg\| <math>c=3</math>
			</gallery>

	Figure 9 shows a single bounce mode where each bounce is the same length as the previous one. This is seen by the single grouping of points along the one to one line. Figure 10, shows a two bounce mode where two distinct bounces are seen on either side of the one to one line. Both of these return diagrams can be inferred from looking at the bifurcation diagram. Figure 11 shows the return diagram for a more interesting region. In the region of $\Gamma$ = 3.5 the bifurcation diagram looks very chaotic; however, the return map shows clear patterns in the data. A bimodal curve is seen in the bifurcation diagram indication complex behaving is being observed.		Figure 9 shows a single bounce mode where each bounce is the same length as the previous one. This is seen by the single grouping of points along the one to one line. Figure 10, shows a two bounce mode where two distinct bounces are seen on either side of the one to one line. Both of these return diagrams can be inferred from looking at the bifurcation diagram. Figure 11 shows the return diagram for a more interesting region. In the region of $\Gamma$ = 3.5 the bifurcation diagram looks very chaotic; however, the return map shows clear patterns in the data. A bimodal curve is seen in the bifurcation diagram indication complex behaving is being observed.

Group3 at 17:00, 16 December 2011

2011-12-16T17:00:37Z

Group3 at 16:58, 16 December 2011

2011-12-16T16:58:40Z

← Older revision		Revision as of 12:58, 16 December 2011
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	Data acquisition was handled using Lab View software. Data was recorded at 20 KHz in two channels; plate acceleration and voltage from the continuity sensor. The data was output from Labview in a tab delimited format with four columns. An additional column was added to the data containing the time stamp for each measurement. The Figure 6 shows a block diagram of the informational flow.		Data acquisition was handled using Lab View software. Data was recorded at 20 KHz in two channels; plate acceleration and voltage from the continuity sensor. The data was output from Labview in a tab delimited format with four columns. An additional column was added to the data containing the time stamp for each measurement. The Figure 6 shows a block diagram of the informational flow.

	[[File: expodiagram.JPG \| 400px \| thumb \| ~~center~~ \| Experimental setup ]]		[[File: expodiagram.JPG \| 400px \| thumb \| right \| Experimental setup ]]

	LabView was used to control the vibrating plate. LabView output the driving signal oscillating between -2.5 and 2.5 V. The signal was then passed through an amplifier whose gain was adjusted such that the minimum and maximum accelerations desired could be achieved. Data was taken by continuously increasing the amplitude of the voltage applied to the shaker table such that the acceleration slowly increased from 0g to 8g. Physically, this adjusted $\Gamma$ by increasing the amplitude of vibration while maintaining a constant frequency. This was done in steps where a constant maximum amplitude was held for a specified number of cycles. The number of cycles was control by the user. Each period of constant amplitude vibration represents a slice of the bifurcation diagram. The data from each set of constant amplitude readings was analysed independently to find the time of flight in each region then assembled into the bifurcation diagram. It is advantageous to hold the acceleration constant for longer periods of time, more cycles, so that transients can die out and more data is available. However, this results in very long experiment durations and large data files that are difficult to handle. The number of cycles held at each amplitude was varied from 5 to 60. Figure 7 shows regions of constant amplitude oscillation increasing in steps		LabView was used to control the vibrating plate. LabView output the driving signal oscillating between -2.5 and 2.5 V. The signal was then passed through an amplifier whose gain was adjusted such that the minimum and maximum accelerations desired could be achieved. Data was taken by continuously increasing the amplitude of the voltage applied to the shaker table such that the acceleration slowly increased from 0g to 8g. Physically, this adjusted $\Gamma$ by increasing the amplitude of vibration while maintaining a constant frequency. This was done in steps where a constant maximum amplitude was held for a specified number of cycles. The number of cycles was control by the user. Each period of constant amplitude vibration represents a slice of the bifurcation diagram. The data from each set of constant amplitude readings was analysed independently to find the time of flight in each region then assembled into the bifurcation diagram. It is advantageous to hold the acceleration constant for longer periods of time, more cycles, so that transients can die out and more data is available. However, this results in very long experiment durations and large data files that are difficult to handle. The number of cycles held at each amplitude was varied from 5 to 60. Figure 7 shows regions of constant amplitude oscillation increasing in steps

	[[File: steps.JPG \| 400px \| thumb \| ~~center~~ \| Experimental setup ]]		[[File: steps.JPG \| 400px \| thumb \| right \| Experimental setup ]]

	The data was analysed by looking at each group of constant amplitude vibrations independently. The time of flight was measured for each bounce and the initial 10 bounces were ignored. This allows for transients to die out. It is not necessary to eliminate many cycles because once the ball reaches a sticking region all the previous bounces are forgotten.		The data was analysed by looking at each group of constant amplitude vibrations independently. The time of flight was measured for each bounce and the initial 10 bounces were ignored. This allows for transients to die out. It is not necessary to eliminate many cycles because once the ball reaches a sticking region all the previous bounces are forgotten.
Line 148:		Line 148:
	In the higher acceleration regions of the bifurcation diagrams we see that things become more chaotic. To look for more patterns in the data that may not be visible in the bifurcation diagram, return maps were generated to visualize the relationship between the time of flight for the current bounce and the one preceding it. Return maps for $\Gamma$ of 1.75, 2.25, and 3.5g are shown in Figures 9, 10 and 11.		In the higher acceleration regions of the bifurcation diagrams we see that things become more chaotic. To look for more patterns in the data that may not be visible in the bifurcation diagram, return maps were generated to visualize the relationship between the time of flight for the current bounce and the one preceding it. Return maps for $\Gamma$ of 1.75, 2.25, and 3.5g are shown in Figures 9, 10 and 11.

	[[File: singlebouncemode.JPG]]		[[File: singlebouncemode.JPG \| 400px \| thumb \| center \| Experimental setup ]]
			[[File: twobouncemode.JPG \| 400px \| thumb \| center \| Experimental setup ]]
			[[File: bimodalmode.JPG \| 400px \| thumb \| center \| Experimental setup ]]

	~~[[File: twobouncemode.JPG]]~~

	~~[[File: bimodalmode.JPG]]~~

← Older revision		Revision as of 13:00, 16 December 2011
Line 128:		Line 128:
	Data acquisition was handled using Lab View software. Data was recorded at 20 KHz in two channels; plate acceleration and voltage from the continuity sensor. The data was output from Labview in a tab delimited format with four columns. An additional column was added to the data containing the time stamp for each measurement. The Figure 6 shows a block diagram of the informational flow.		Data acquisition was handled using Lab View software. Data was recorded at 20 KHz in two channels; plate acceleration and voltage from the continuity sensor. The data was output from Labview in a tab delimited format with four columns. An additional column was added to the data containing the time stamp for each measurement. The Figure 6 shows a block diagram of the informational flow.

	[[File: expodiagram.JPG \| 400px \| thumb \| right \| ~~Experimental setup~~ ]]		[[File: expodiagram.JPG \| 400px \| thumb \| right \| Data flow block diagram ]]

	LabView was used to control the vibrating plate. LabView output the driving signal oscillating between -2.5 and 2.5 V. The signal was then passed through an amplifier whose gain was adjusted such that the minimum and maximum accelerations desired could be achieved. Data was taken by continuously increasing the amplitude of the voltage applied to the shaker table such that the acceleration slowly increased from 0g to 8g. Physically, this adjusted $\Gamma$ by increasing the amplitude of vibration while maintaining a constant frequency. This was done in steps where a constant maximum amplitude was held for a specified number of cycles. The number of cycles was control by the user. Each period of constant amplitude vibration represents a slice of the bifurcation diagram. The data from each set of constant amplitude readings was analysed independently to find the time of flight in each region then assembled into the bifurcation diagram. It is advantageous to hold the acceleration constant for longer periods of time, more cycles, so that transients can die out and more data is available. However, this results in very long experiment durations and large data files that are difficult to handle. The number of cycles held at each amplitude was varied from 5 to 60. Figure 7 shows regions of constant amplitude oscillation increasing in steps		LabView was used to control the vibrating plate. LabView output the driving signal oscillating between -2.5 and 2.5 V. The signal was then passed through an amplifier whose gain was adjusted such that the minimum and maximum accelerations desired could be achieved. Data was taken by continuously increasing the amplitude of the voltage applied to the shaker table such that the acceleration slowly increased from 0g to 8g. Physically, this adjusted $\Gamma$ by increasing the amplitude of vibration while maintaining a constant frequency. This was done in steps where a constant maximum amplitude was held for a specified number of cycles. The number of cycles was control by the user. Each period of constant amplitude vibration represents a slice of the bifurcation diagram. The data from each set of constant amplitude readings was analysed independently to find the time of flight in each region then assembled into the bifurcation diagram. It is advantageous to hold the acceleration constant for longer periods of time, more cycles, so that transients can die out and more data is available. However, this results in very long experiment durations and large data files that are difficult to handle. The number of cycles held at each amplitude was varied from 5 to 60. Figure 7 shows regions of constant amplitude oscillation increasing in steps

	[[File: steps.JPG \| 400px \| thumb \| right \| ~~Experimental setup~~ ]]		[[File: steps.JPG \| 400px \| thumb \| right \| Steps of constant amplitude vibrations ]]

	The data was analysed by looking at each group of constant amplitude vibrations independently. The time of flight was measured for each bounce and the initial 10 bounces were ignored. This allows for transients to die out. It is not necessary to eliminate many cycles because once the ball reaches a sticking region all the previous bounces are forgotten.		The data was analysed by looking at each group of constant amplitude vibrations independently. The time of flight was measured for each bounce and the initial 10 bounces were ignored. This allows for transients to die out. It is not necessary to eliminate many cycles because once the ball reaches a sticking region all the previous bounces are forgotten.
Line 140:		Line 140:
	Assembling the time of flights for each acceleration and plotting the time of flight against $\Gamma$ gives the bifurcation diagram. The full diagram is shown in Figure 8.		Assembling the time of flights for each acceleration and plotting the time of flight against $\Gamma$ gives the bifurcation diagram. The full diagram is shown in Figure 8.

	[[File: bifurcationdiagram.JPG \| 400px \| thumb \| center \| ~~Experimental setup~~ ]]		[[File: bifurcationdiagram.JPG \| 400px \| thumb \| center \| Measured Bifurcation Diagram ]]

	Looking at the bifurcation diagram, we see the single bounce branch of the bifurcation diagram start right around 1g where we expect the ball to start bouncing. The first bifurcation occurs around 2g. This is somewhat lower than predicted. At the bifurcation we see cascades of time of flights which are multi bounce modes that are short lived. The upper ridge of the bifurcation diagram represents the single bounce mode and it mimics the predicted diagram. The measured time of flights are within a factor of 2 of the predicted values. There are also the same regions of infeasibility as seen in the predicted diagrams.		Looking at the bifurcation diagram, we see the single bounce branch of the bifurcation diagram start right around 1g where we expect the ball to start bouncing. The first bifurcation occurs around 2g. This is somewhat lower than predicted. At the bifurcation we see cascades of time of flights which are multi bounce modes that are short lived. The upper ridge of the bifurcation diagram represents the single bounce mode and it mimics the predicted diagram. The measured time of flights are within a factor of 2 of the predicted values. There are also the same regions of infeasibility as seen in the predicted diagrams.
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	In the higher acceleration regions of the bifurcation diagrams we see that things become more chaotic. To look for more patterns in the data that may not be visible in the bifurcation diagram, return maps were generated to visualize the relationship between the time of flight for the current bounce and the one preceding it. Return maps for $\Gamma$ of 1.75, 2.25, and 3.5g are shown in Figures 9, 10 and 11.		In the higher acceleration regions of the bifurcation diagrams we see that things become more chaotic. To look for more patterns in the data that may not be visible in the bifurcation diagram, return maps were generated to visualize the relationship between the time of flight for the current bounce and the one preceding it. Return maps for $\Gamma$ of 1.75, 2.25, and 3.5g are shown in Figures 9, 10 and 11.

	[[File: singlebouncemode.JPG \| 400px \| thumb \| ~~center~~ \| ~~Experimental setup~~ ]]		[[File: singlebouncemode.JPG \| 400px \| thumb \| left \| Return Map of Gamma = 1.75 ]]
	[[File: twobouncemode.JPG \| 400px \| thumb \| center \| ~~Experimental setup~~ ]]		[[File: twobouncemode.JPG \| 400px \| thumb \| center \| Return Map of Gamma = 2.25 ]]
	[[File: bimodalmode.JPG \| 400px \| thumb \| ~~center~~ \| ~~Experimental setup~~ ]]		[[File: bimodalmode.JPG \| 400px \| thumb \| right \| Return Map of Gamma = 3.75 ]]