Modified Gyroscope - Revision history

Schuetz2 at 05:35, 17 June 2025

2025-06-17T05:35:21Z

← Older revision		Revision as of 05:35, 17 June 2025
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	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	::The MORwiki Community, '''Modified Gyroscope'''. MORwiki - Model Order Reduction Wiki, 2018. ~~http~~://modelreduction.org/~~index.php~~/Modified_Gyroscope		::The MORwiki Community, '''Modified Gyroscope'''. MORwiki - Model Order Reduction Wiki, 2018. https://modelreduction.org/morwiki/Modified_Gyroscope

	@MISC{morwiki_modgyro,		@MISC{morwiki_modgyro,
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	title = {Modified Gyroscope},		title = {Modified Gyroscope},
	howpublished = {{MORwiki} -- Model Order Reduction Wiki},		howpublished = {{MORwiki} -- Model Order Reduction Wiki},
	url = <nowiki>{~~http~~://modelreduction.org/~~index.php~~/Modified_Gyroscope}</nowiki>,		url = <nowiki>{https://modelreduction.org/morwiki/Modified_Gyroscope}</nowiki>,
	year = 2018		year = 2018
	}		}

Malhotra: infobox string

2023-11-30T09:36:43Z

infobox string

← Older revision		Revision as of 09:36, 30 November 2023
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	[[Category:second differential order]]		[[Category:second differential order]]

			{{Infobox
			\|Title = Modified Gyroscope
			\|Benchmark ID = modifiedGyroscope_n17931m1q1
			\|Category = misc
			\|System-Class = AP-LTI-SOS
			\|nstates = 17931
			\|ninputs = 1
			\|noutputs = 1
			\|nparameters = 3
			\|components = B, C, E, K, M
			\|License = NA
			\|Creator = [[User:Feng]]
			\|Editor =
			* [[User:Feng]]
			* [[User:Himpe]]
			* [[User:Will]]
			* [[User:Saak]]
			* [[User:Lund]]
			\|Zenodo-link = NA
			}}

	==Description==		==Description==

Lund: /* Data */ Clarify how matrix names are changed for MORB

2023-05-11T08:45:29Z

Data: Clarify how matrix names are changed for MORB

← Older revision		Revision as of 08:45, 11 May 2023
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	The model is generated in ANSYS.		The model is generated in ANSYS.
	The system matrices <math>M, \, ~~M_1~~, \, ~~E_1~~, \, ~~E_2~~, \, K, \, ~~K_1~~, \,~~K_2~~</math>, and <math> B</math> are in the [http://math.nist.gov/MatrixMarket/ MatrixMarket format], and can be downloaded here: [[Media: Gyroscope_modi.tgz\|Gyroscope_modi.tgz]].		The system matrices <math>M_1, \, M_2, \, D_1, \, D_2, \, T_1, \, T_2, \, T_3</math>, and <math> B</math> are in the [http://math.nist.gov/MatrixMarket/ MatrixMarket format], and can be downloaded here: [[Media: Gyroscope_modi.tgz\|Gyroscope_modi.tgz]]. The matrix <math>C</math> defines the output, which has zeros on all the entries, except on the 2315th entry, where the value is <math>-1</math>, and on the 5806th entry, the value is <math>1</math>;
	The matrix <math>C</math> defines the output, which has zeros on all the entries, except on the 2315th entry, where the value is <math>-1</math>, and on the 5806th entry, the value is <math>1</math>;
	in MATLAB notation, it is <tt>C(1,2315) = -1</tt> and <tt>C(1,5806) = 1</tt>.		in MATLAB notation, it is <tt>C(1,2315) = -1</tt> and <tt>C(1,5806) = 1</tt>.

	The matrices have been reindexed for [[MORB]], as shown in the next section.		The matrices have been reindexed for [[MORB]], as shown in the next section. In particular, <math>D_i</math> is denoted instead by <math>E_i</math>, and <math>T_i</math> by <math>K_i</math>.

	==Dimensions==		==Dimensions==

Lund: /* The Parametrized Model */ Update matrices to match what is stored in matrix market file

2023-05-11T08:43:49Z

The Parametrized Model: Update matrices to match what is stored in matrix market file

← Older revision		Revision as of 08:43, 11 May 2023
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	:<math>		:<math>
	\begin{align}		\begin{align}
	M(d)\ddot{x}(t) +E(d,\theta)\dot{x}(t) +K(d)x(t) &= B, \\		M(d)\ddot{x}(t) +D(d,\theta)\dot{x}(t) +T(d)x(t) &= B, \\
	y(t) &=Cx(t).		y(t) &=Cx(t).
	\end{align}		\end{align}
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	Here,		Here,

	* <math>M(d)=M + ~~dM_1~~\in \mathbb R^{n\times n}</math> is the mass matrix,		* <math>M(d)=M_1 + dM_2\in \mathbb R^{n\times n}</math> is the mass matrix,
	* <math>E(d,\theta)=\theta(~~E_1~~ + d ~~E_2~~)\in \mathbb R^{n\times n}</math> is the damping matrix,		* <math>D(d,\theta)=\theta(D_1 + d D_2)\in \mathbb R^{n\times n}</math> is the damping matrix,
	* <math>K(d)=K+(1/d)~~K_1~~+~~dK_2~~\in \mathbb R^{n\times n}</math> is the stiffness matrix,		* <math>T(d)=T_1+(1/d)T_2+dT_3\in \mathbb R^{n\times n}</math> is the stiffness matrix,
	* <math>B \in \mathbb R^{n \times 1}</math> is the load vector,		* <math>B \in \mathbb R^{n \times 1}</math> is the load vector,
	* <math>C \in \mathbb R^{1 \times n}</math> is the output matrix,		* <math>C \in \mathbb R^{1 \times n}</math> is the output matrix,
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	* and <math>y \in \mathbb R </math> is the output response.		* and <math>y \in \mathbb R </math> is the output response.

	The quantity of ~~interesting~~ <math>y</math> of the system is <math>\delta z(t)</math>,		The quantity of interest <math>y</math> of the system is <math>\delta z(t)</math>, which is the difference of the displacement <math>z(t)</math> between the two red markings on the ''east'' side of the bearing (see <xr id="fig:gyro"/>).
	which is the difference of the displacement <math>z(t)</math> between the two red markings on the ''east'' side of the bearing (see <xr id="fig:gyro"/>).

	The parameters of the system, <math>d</math> and <math>\theta</math>,		The parameters of the system, <math>d</math> and <math>\theta</math>, represent the width of the bearing(<math>d</math>) and the rotation velocity along the <math>x</math>-axis (<math>\theta</math>), with the ranges: <math>\theta\in [10^{-7}, 10^{-5}]</math> and <math>d\in [1,2]</math>.
	represent the width of the bearing(<math>d</math>) and the rotation velocity along the <math>x</math>-axis (<math>\theta</math>),
	with the ranges: <math>\theta\in [10^{-7}, 10^{-5}]</math> and <math>d\in [1,2]</math>.

	The device works in the frequency range <math>f \in [0.025, 0.25]</math>MHz and the degrees of freedom are <math>n = 17913</math>.		The device works in the frequency range <math>f \in [0.025, 0.25]</math>MHz and the degrees of freedom are <math>n = 17913</math>.

Lund: /* Dimensions */ missing _

2023-05-09T14:56:18Z

Dimensions: missing _

← Older revision		Revision as of 14:56, 9 May 2023
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	System dimensions:		System dimensions:

	<math>M_{1,2}, E_{1,2}, K{1,2,3} \in \mathbb{R}^{17931 \times 17931}</math>,		<math>M_{1,2}, E_{1,2}, K_{1,2,3} \in \mathbb{R}^{17931 \times 17931}</math>,
	<math>B \in \mathbb{R}^{17931 \times 1}</math>,		<math>B \in \mathbb{R}^{17931 \times 1}</math>,
	<math>C \in \mathbb{R}^{1 \times 17931}</math>.		<math>C \in \mathbb{R}^{1 \times 17931}</math>.

Lund: /* Dimensions */ re-index matrices

2023-05-09T14:56:02Z

Dimensions: re-index matrices

← Older revision		Revision as of 14:56, 9 May 2023
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	:<math>		:<math>
	\begin{array}{rcl}		\begin{array}{rcl}
	(M + d ~~M_1~~)\ddot{x}(t) + \theta(E_1 + d E_2) \dot{x}(t) + (K + d^{-1} ~~K_1~~ + d ~~K_2~~)x(t) &=& B \\		(M_1 + d M_2)\ddot{x}(t) + \theta(E_1 + d E_2) \dot{x}(t) + (K_1 + d^{-1} K_2 + d K_3)x(t) &=& B \\
	y(t) &=& Cx(t)		y(t) &=& Cx(t)
	\end{array}		\end{array}
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	System dimensions:		System dimensions:

	<math>M, ~~M_1~~, ~~E_1~~, ~~E_2~~, K, ~~K_1~~, ~~K_2~~ \in \mathbb{R}^{17931 \times 17931}</math>,		<math>M_{1,2}, E_{1,2}, K{1,2,3} \in \mathbb{R}^{17931 \times 17931}</math>,
	<math>B \in \mathbb{R}^{17931 \times 1}</math>,		<math>B \in \mathbb{R}^{17931 \times 1}</math>,
	<math>C \in \mathbb{R}^{1 \times 17931}</math>.		<math>C \in \mathbb{R}^{1 \times 17931}</math>.

Lund: /* Data */ comment on re-indexing

2023-05-09T14:55:09Z

Data: comment on re-indexing

← Older revision		Revision as of 14:55, 9 May 2023
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	The matrix <math>C</math> defines the output, which has zeros on all the entries, except on the 2315th entry, where the value is <math>-1</math>, and on the 5806th entry, the value is <math>1</math>;		The matrix <math>C</math> defines the output, which has zeros on all the entries, except on the 2315th entry, where the value is <math>-1</math>, and on the 5806th entry, the value is <math>1</math>;
	in MATLAB notation, it is <tt>C(1,2315) = -1</tt> and <tt>C(1,5806) = 1</tt>.		in MATLAB notation, it is <tt>C(1,2315) = -1</tt> and <tt>C(1,5806) = 1</tt>.

			The matrices have been reindexed for [[MORB]], as shown in the next section.

	==Dimensions==		==Dimensions==

Lund: update matrix names to match Models

2023-04-20T19:50:59Z

update matrix names to match Models

← Older revision		Revision as of 19:50, 20 April 2023
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	:<math>		:<math>
	\begin{align}		\begin{align}
	M(d)\ddot{x}(t) +D(d,\theta)\dot{x}(t) +T(d)x(t) &= B, \\		M(d)\ddot{x}(t) +E(d,\theta)\dot{x}(t) +K(d)x(t) &= B, \\
	y(t) &=Cx(t).		y(t) &=Cx(t).
	\end{align}		\end{align}
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	Here,		Here,

	* <math>M(d)=~~(M_1~~+~~dM_2)~~\in \mathbb R^{n\times n}</math> is the mass matrix,		* <math>M(d)=M + dM_1\in \mathbb R^{n\times n}</math> is the mass matrix,
	* <math>D(d,\theta)=\theta(~~D_1~~ + d ~~D_2~~)\in \mathbb R^{n\times n}</math> is the damping matrix,		* <math>E(d,\theta)=\theta(E_1 + d E_2)\in \mathbb R^{n\times n}</math> is the damping matrix,
	* <math>T(d)=~~T_1~~+(1/d)~~T_2~~+~~dT_3~~\in \mathbb R^{n\times n}</math> is the stiffness matrix,		* <math>K(d)=K+(1/d)K_1+dK_2\in \mathbb R^{n\times n}</math> is the stiffness matrix,
	* <math>B \in \mathbb R^{n \times 1}</math> is the load vector,		* <math>B \in \mathbb R^{n \times 1}</math> is the load vector,
	* <math>C \in \mathbb R^{1 \times n}</math> is the output matrix,		* <math>C \in \mathbb R^{1 \times n}</math> is the output matrix,
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	The model is generated in ANSYS.		The model is generated in ANSYS.
	The system matrices <math>~~M_1~~, \, ~~M_2~~, \, ~~D_1~~, \, ~~D_2~~, \, ~~T_1~~, \, ~~T_2~~, \,~~T_3~~</math>, and <math> B</math> are in the [http://math.nist.gov/MatrixMarket/ MatrixMarket format], and can be downloaded here: [[Media: Gyroscope_modi.tgz\|Gyroscope_modi.tgz]].		The system matrices <math>M, \, M_1, \, E_1, \, E_2, \, K, \, K_1, \,K_2</math>, and <math> B</math> are in the [http://math.nist.gov/MatrixMarket/ MatrixMarket format], and can be downloaded here: [[Media: Gyroscope_modi.tgz\|Gyroscope_modi.tgz]].
	The matrix <math>C</math> defines the output, which has zeros on all the entries, except on the 2315th entry, where the value is <math>-1</math>, and on the 5806th entry, the value is <math>1</math>;		The matrix <math>C</math> defines the output, which has zeros on all the entries, except on the 2315th entry, where the value is <math>-1</math>, and on the 5806th entry, the value is <math>1</math>;
	in MATLAB notation, it is <tt>C(1,2315) = -1</tt> and <tt>C(1,5806) = 1</tt>.		in MATLAB notation, it is <tt>C(1,2315) = -1</tt> and <tt>C(1,5806) = 1</tt>.
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	:<math>		:<math>
	\begin{array}{rcl}		\begin{array}{rcl}
	(~~M_1~~ + d ~~M_2~~)\ddot{x}(t) + \theta(~~D_1~~ + d ~~D_2~~) \dot{x}(t) + (~~T_1~~ + d^{-1} ~~T_2~~ + d ~~T_3~~)x(t) &=& B \\		(M + d M_1)\ddot{x}(t) + \theta(E_1 + d E_2) \dot{x}(t) + (K + d^{-1} K_1 + d K_2)x(t) &=& B \\
	y(t) &=& Cx(t)		y(t) &=& Cx(t)
	\end{array}		\end{array}
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	System dimensions:		System dimensions:

	<math>M_1, ~~M_2, D_1~~, ~~D_2~~, ~~T_1~~, ~~T_2~~, ~~T_3~~ \in \mathbb{R}^{17931 \times 17931}</math>,		<math>M, M_1, E_1, E_2, K, K_1, K_2 \in \mathbb{R}^{17931 \times 17931}</math>,
	<math>B \in \mathbb{R}^{17931 \times 1}</math>,		<math>B \in \mathbb{R}^{17931 \times 1}</math>,
	<math>C \in \mathbb{R}^{1 \times 17931}</math>.		<math>C \in \mathbb{R}^{1 \times 17931}</math>.

Himpe at 13:00, 25 August 2022

2022-08-25T13:00:56Z

← Older revision		Revision as of 13:00, 25 August 2022
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	[[Category:ODE]]		[[Category:ODE]]
	[[Category:linear]]		[[Category:linear]]
	[[Category:~~parametric 2-5 parameters~~]]		[[Category:Parametric]]
	[[Category:affine parameter representation]]		[[Category:affine parameter representation]]
	[[Category:time invariant]]		[[Category:time invariant]]

Himpe: Fix CrossRefs

2021-08-27T07:45:29Z

Fix CrossRefs

← Older revision		Revision as of 07:45, 27 August 2021
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	The basic working principle of the '''gyroscope''' can be described as follows, see also <ref name="Moo07"/>.		The basic working principle of the '''gyroscope''' can be described as follows, see also <ref name="Moo07"/>.
	Without applied external rotation, the paddles vibrate in phase with the function <math>z(t),</math> see ~~<xr id="fig:gyro"/>~~.		Without applied external rotation, the paddles vibrate in phase with the function <math>z(t),</math> see Fig. 1.
	Under the influence of an external rotation about the <math>x</math>-axis (drawn in red),		Under the influence of an external rotation about the <math>x</math>-axis (drawn in red),
	an additional force due to the Coriolis acceleration acts upon the paddles.		an additional force due to the Coriolis acceleration acts upon the paddles.