Co-ordinate Systems Flashcards

1
Q

Using the “Gangsta” sign gesture for the cross product (AXB), what does the pointer and middle finger & thumb represent?

A

Thumb: A
Pointer Finger: B
Middle Finger: AXB

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2
Q

What does |AXB| equal?

A

Magnitude of AXB = ABsinα

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3
Q

If C=AXB, what is C•A and C•B?

A

0 as they are orthogonal

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4
Q

What is dSx for a Cartesian System?

A

[xhat]dydz

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5
Q

What is dSy for a Cartesian System?

A

[yhat]dxdz

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6
Q

What is dSz for a Cartesian System?

A

[zhat]dxdy

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7
Q

What is dV for a Cartesian System?

A

dxdydz

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8
Q

What is the gradient of F equal to?

A

SEE: [img]http://mathworld.wolfram.com/images/equations/Divergence/NumberedEquation4.gif[/img]

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9
Q

What is Divergence?

A

Divergence is Flux/Volume i.e. Flux per unit Volume

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10
Q

When is flux positive?

A

When leaving a surface

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11
Q

When is flux negative?

A

When entering a surface

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12
Q

What is flux?

A

Flux is the net amount of something passing through a surface

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13
Q

What is it called when the divergence of A is greater than 0?

A

A source

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14
Q

What is it called when the divergence of A is less than 0?

A

A sink

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15
Q

What do we call ϕ?

A

Azimuth

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16
Q

Vector representation of A in Cylindrical Co-Ord system?

A

A= Ar[rhat] + Aϕ[ϕhat] + Az[zhat]

17
Q

What is the length differential in a Cylindrical system?

A

dl= [rhat]dr + [ϕhat]rdϕ + [zhat]dz

18
Q

What is the differential length of an arc formed in the azimuth plane for Cylindrical Co-Ords?

A

rdϕ

19
Q

What is the volume differential dV for a Cylindrical system?

A

dV = rdϕdrdz (All the lengths multiplied)

20
Q

What is dSr for a Cylindrical system?

A

[rhat]rdϕdz

21
Q

What is dSϕ for a Cylindrical system?

A

[ϕhat]drdz

22
Q

What is dSz for a Cylindrical system?

A

[zhat]rdϕdr

23
Q

What is the name of Θ?

A

Zenith angle

24
Q

What is the value of elevation?

A

90-Θ

25
Q

What is the principal plane for r in Spherical Co-Ords?

A

A Circle

26
Q

What is the principal plane for Θ in Spherical Co-Ords?

A

A Cone

27
Q

What is the principal plane for ϕ in Spherical Co-Ords?

A

A plane

28
Q

What is the length differential for in Spherical Co-Ords?

A

dl = [rhat]dr + [Θhat]rdΘ + [ϕhat]rsinΘdϕ

29
Q

What is the formula for a differential arc formed on the ϕ plane in Spherical Co-Ords? (Hint: dependant on r and Θ)

A

rsinΘdϕ

30
Q

What is dSr in Spherical Co-ords?

A

[rhat]r^2sinΘdϕdΘ

31
Q

What is dSΘ in Spherical Co-ords?

A

[Θhat]rsinΘdϕdr

32
Q

What is dSϕ in Spherical Co-ords?

A

[ϕhat]rdΘdr

33
Q

What is dV in Spherical Co-ords?

A

r^2sinΘdΘdrdϕ