Maths - Standards

I am very keen to have consistent standards of notation and terminology across this site. Its hard enough to learn these things without being confused by inconsistent standards. It may not be perfect yet so, if you find any inconsistencies across the site please let me know.

I have documented the maths notation on this page.

I have also tried to apply standards to the physics notation and terminology (see physics standards).

In some cases there are different ways to notate, calculate and display. Wherever possible I have tried to base these on standards, here are some standards used:

	This site	VRML/X3D (ISO/IEC 19775)	OpenGL	DirectX	MathML http://www.w3.org/TR/REC-MathML/
Vector shown as row or column				see D3DVECTOR structure
Matrix order			opposite of everything else	see D3DMATRIX structure
Coordinate System	right-handed cartesian	right-handed cartesian	right-handed cartesian (for orthographic projection)	left-handed cartesian
x,y and z definitions	+X to the right +Y straight up +Z axis toward viewer	+X to the right +Y straight up +Z axis toward viewer	Orthographic Projection see glOrtho() +X to the right +Y straight up +Z axis toward viewer Viewport +X = to the right +Y = top of screen +Z = depth buffer = distance from viewer (range 0 to 1) W = scaling value for perspective transform	+X to the right +Y straight up +Z axis into screen
Euler angles	Heading = rotation about y axis Attitude = rotation about z axis Bank = rotation about x axis
Euler angle order	Heading applied first Attitude applied second Bank applied last
Positive angle	right hand screw	right hand screw	right hand screw (see glRotated)
Angle units	radians	radians	degrees (see glRotated)	radians
Vector Cross product	right hand: x = Ay * Bz - By * Az y = Az * Bx - Bz * Ax z = Ax * By - Bx * Ay so, mechanics equations are, = × = ×
Clifford Algebra: factor ordering	dually
Clifford Algebra: element ordering	grade-ordered

I have tried to use established open standards rather than inventing my own wherever I can.

Where these standards conflict I have used VRML/X3D (ISO/IEC 19775) on this site. For Euler angles I have used NASA standard Aeroplane but I have swapped the y and z axis, to conform to x3d, so:

Heading applied first (rotation about y axis – which is up-down) Attitude applied second (rotation about z axis which is along wing) Bank applied last (rotation about x axis which is front-back)

Although z and y are swapped: Heading, Attitude and Bank are applied in the same order so the properties of NASA standard Aeroplane are still the same, i.e. the singularity still happens at attitude= -+90 degrees.

I mentioned NASA standard Aeroplane (as its American I should have written NASA standard Airplane) . The problem is that I can't actually find this standard even from NASA employees that I have communicated with. The only information that I have about this standard is from a book: Analytical Dynamics (McGraw-Hill International Editions) and this is very limited information. Is unfortunate as a standard from such a source as NASA would be helpful.