Template:Standard linear problem notation - Revision history

Meylan at 04:14, 20 August 2009

2009-08-20T04:14:50Z

← Older revision		Revision as of 04:14, 20 August 2009
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	equations (see [[Linear and Second-Order Wave Theory]]).		equations (see [[Linear and Second-Order Wave Theory]]).
	{{frequency definition}}		{{frequency definition}}
	~~The water motion is represented by a~~ velocity potential ~~which is~~		{{velocity potential in frequency domain}}
	~~denoted by <math>\phi\,</math>.~~ The coordinate system is the standard Cartesian coordinate system		The coordinate system is the standard Cartesian coordinate system
	with the <math>z-</math>axis pointing vertically up. The water surface is at		with the <math>z-</math>axis pointing vertically up. The water surface is at
	<math>z=0</math> and the region of interest is		<math>z=0</math> and the region of interest is

Meylan at 09:05, 19 August 2009

2009-08-19T09:05:26Z

← Older revision		Revision as of 09:05, 19 August 2009
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	We assume small amplitude so that we can linearise all the		We assume small amplitude so that we can linearise all the
	equations (see [[Linear and Second-Order Wave Theory]]). ~~We also assume that [[Frequency Domain Problem]] with~~ frequency ~~<math>\omega</math>~~		equations (see [[Linear and Second-Order Wave Theory]]).
	~~and we assume that all variables are proportional to~~		{{frequency definition}}
	~~<center>~~
	~~<math>\exp(i\omega t)\,</math>~~
	~~</center>~~
	The water motion is represented by a velocity potential which is		The water motion is represented by a velocity potential which is
	denoted by <math>\phi\,</math>. The coordinate system is the standard Cartesian coordinate system		denoted by <math>\phi\,</math>. The coordinate system is the standard Cartesian coordinate system

Adi Kurniawan at 01:41, 31 March 2009

2009-03-31T01:41:54Z

← Older revision		Revision as of 01:41, 31 March 2009
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	The water motion is represented by a velocity potential which is		The water motion is represented by a velocity potential which is
	denoted by <math>\phi\,</math>. The coordinate system is the standard Cartesian coordinate system		denoted by <math>\phi\,</math>. The coordinate system is the standard Cartesian coordinate system
	with the <math>z</math> axis pointing vertically up. The water surface is at		with the <math>z-</math>axis pointing vertically up. The water surface is at
	<math>z=0</math> and the region of interest is		<math>z=0</math> and the region of interest is
	<math>-h<z<0</math>. There is a body which occupies the region <math>\Omega</math>		<math>-h<z<0</math>. There is a body which occupies the region <math>\Omega</math>
	and we ~~denoted~~ the wetted surface of the body by <math>\partial\Omega</math>		and we denote the wetted surface of the body by <math>\partial\Omega</math>
	We denote <math>\mathbf{r}=(x,y)</math> as the horizontal coordinate in two or three dimensions		We denote <math>\mathbf{r}=(x,y)</math> as the horizontal coordinate in two or three dimensions
	respectively and the ~~cartesian~~ system we denote by <math>\mathbf{x}</math>.		respectively and the Cartesian system we denote by <math>\mathbf{x}</math>.
	We assume that the bottom surface is of constant depth at <math>z=-h</math>.		We assume that the bottom surface is of constant depth at <math>z=-h</math>.

Meylan at 22:50, 22 March 2009

2009-03-22T22:50:13Z

← Older revision		Revision as of 22:50, 22 March 2009
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	</center>		</center>
	The water motion is represented by a velocity potential which is		The water motion is represented by a velocity potential which is
	denoted by <math>\phi</math>. The coordinate system is the standard Cartesian coordinate system		denoted by <math>\phi\,</math>. The coordinate system is the standard Cartesian coordinate system
	with the <math>z</math> axis pointing vertically up. The water surface is at		with the <math>z</math> axis pointing vertically up. The water surface is at
	<math>z=0</math> and the region of interest is		<math>z=0</math> and the region of interest is

Adi Kurniawan at 07:32, 24 February 2009

2009-02-24T07:32:53Z

← Older revision		Revision as of 07:32, 24 February 2009
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	and we assume that all variables are proportional to		and we assume that all variables are proportional to
	<center>		<center>
	<math>\exp(i\omega t)</math>		<math>\exp(i\omega t)\,</math>
	</center>		</center>
	The water motion is represented by a velocity potential which is		The water motion is represented by a velocity potential which is

Meylan at 08:58, 13 September 2008

2008-09-13T08:58:29Z

← Older revision		Revision as of 08:58, 13 September 2008
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	We assume small amplitude so that we can linearise all the		We assume small amplitude so that we can linearise all the
	equations (see [[Linear and Second-Order Wave Theory]]). We also assume that [[Frequency Domain Problem]] with frequency <math>\omega</math>		equations (see [[Linear and Second-Order Wave Theory]]). We also assume that [[Frequency Domain Problem]] with frequency <math>\omega</math>
			and we assume that all variables are proportional to
			<center>
			<math>\exp(i\omega t)</math>
			</center>
	The water motion is represented by a velocity potential which is		The water motion is represented by a velocity potential which is
	denoted by <math>\phi</math>. The coordinate system is the standard Cartesian coordinate system		denoted by <math>\phi</math>. The coordinate system is the standard Cartesian coordinate system

Meylan at 08:55, 13 September 2008

2008-09-13T08:55:50Z

← Older revision		Revision as of 08:55, 13 September 2008
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	We assume small amplitude so that we can linearise all the		We assume small amplitude so that we can linearise all the
	equations. We also assume that [[Frequency Domain Problem]] with frequency <math>\omega</math>		equations (see [[Linear and Second-Order Wave Theory]]). We also assume that [[Frequency Domain Problem]] with frequency <math>\omega</math>
	The water motion is represented by a velocity potential which is		The water motion is represented by a velocity potential which is
	denoted by <math>\phi</math>. The coordinate system is the standard Cartesian coordinate system		denoted by <math>\phi</math>. The coordinate system is the standard Cartesian coordinate system

Meylan at 08:53, 24 August 2008

2008-08-24T08:53:20Z

← Older revision		Revision as of 08:53, 24 August 2008
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	We denote <math>\mathbf{r}=(x,y)</math> as the horizontal coordinate in two or three dimensions		We denote <math>\mathbf{r}=(x,y)</math> as the horizontal coordinate in two or three dimensions
	respectively and the cartesian system we denote by <math>\mathbf{x}</math>.		respectively and the cartesian system we denote by <math>\mathbf{x}</math>.
	We assume that the bottom surface is of constant depth <math>h</math>.		We assume that the bottom surface is of constant depth at <math>z=-h</math>.

Meylan at 07:30, 24 August 2008

2008-08-24T07:30:58Z

← Older revision		Revision as of 07:30, 24 August 2008
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	We denote <math>\mathbf{r}=(x,y)</math> as the horizontal coordinate in two or three dimensions		We denote <math>\mathbf{r}=(x,y)</math> as the horizontal coordinate in two or three dimensions
	respectively and the cartesian system we denote by <math>\mathbf{x}</math>.		respectively and the cartesian system we denote by <math>\mathbf{x}</math>.
	We assume that the bottom surface is of constant depth ~~but [[Variable Bottom Topography]]~~		We assume that the bottom surface is of constant depth <math>h</math>.
	~~can easily be included~~.

Meylan at 07:30, 24 August 2008

2008-08-24T07:30:16Z

New page

We assume small amplitude so that we can linearise all the
equations. We also assume that [[Frequency Domain Problem]] with frequency <math>\omega</math>
The water motion is represented by a velocity potential which is
denoted by <math>\phi</math>. The coordinate system is the standard Cartesian coordinate system
with the <math>z</math> axis pointing vertically up. The water surface is at
<math>z=0</math> and the region of interest is
<math>-h<z<0</math>. There is a body which occupies the region <math>\Omega</math>
and we denoted the wetted surface of the body by <math>\partial\Omega</math>
We denote <math>\mathbf{r}=(x,y)</math> as the horizontal coordinate in two or three dimensions
respectively and the cartesian system we denote by <math>\mathbf{x}</math>.
We assume that the bottom surface is of constant depth but [[Variable Bottom Topography]]
can easily be included.