Conversion of Unit Vectors - Edubirdie

University:
Santa Fe College
Course:
PHY 2048 | General Physics 1 with Calculus
Academic year:

2024
Views:

134

Pages:

3
Author:

Jabin F.

Conversion of unit vectors 1. spherical polar unit rector into Cartesian Unit vector (r,θ,ϕ)→(x,y,z) r^=cosθz^+sinθ(cosϕx^+sinϕy^) If we put 𝐴 ( 𝑟 , 𝜋 / 2 , 𝜋 / 2 ) A(r,π/2,π/2) then r^=y^ θ^=cos(90∘+θ)z^+cosθ(cosϕx^+sinϕy^)=−sinθz^+cosθ(cosϕx^+sinϕy^) ϕ^=cos(90∘+ϕ)x^+cosϕy^ ⇒ϕ^=−sinϕx^+cosϕy^ Matrix transformation: ( 𝑥 𝑦 𝑧 ) = ( sin ⁡ 𝜃 cos ⁡ 𝜙 sin ⁡ 𝜃 sin ⁡ 𝜙 cos ⁡ 𝜃 cos ⁡ 𝜃 cos ⁡ 𝜙 cos ⁡ 𝜃 sin ⁡ 𝜙 − sin ⁡ 𝜃 − sin ⁡ 𝜙 cos ⁡ 𝜙 0 ) ( 𝑥 ^ 𝑦 ^ 𝑧 ^ ) x y z = sinθcosϕ cosθcosϕ −sinϕ sinθsinϕ cosθsinϕ cosϕ cosθ −sinθ 0 x ^ y ^ z ^ Cylindrical Unit Vector into Cartesian s^=cosϕx^+sinϕy^ ^=−sinϕx^+cosϕy^ z^=+z^ cosϕ=x2+y2x s^ϕ^z^=cosϕ−sinϕ0sinϕcosϕ0001x^y^z^

Related Documents

Conversion of Unit Vectors

Conversion of Unit Vectors - Page 1

Conversion of Unit Vectors - Page 2

Conversion of Unit Vectors - Page 3

of 3

Recommended Documents

Degeneracy Discriminant Factor

Degeneracy Discriminant Factor

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Maxwell's Velocity Distribution

Maxwell's Velocity Distribution

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Answer Key # 1 The Gibbs Free Energy

Answer Key # 1 The Gibbs Free Energy

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Answer Key

General Physics: Answer Key # 23

General Physics: Answer Key # 23

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Answer Key

Rules for Multiplication

Rules for Multiplication

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Basis Physics Notes

Basis Physics Notes

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Physically meaning of scalar product

Physically meaning of scalar product

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Eigen Value

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Anti Hermitten Operator

Anti Hermitten Operator

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Projection Operator

Projection Operator

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Singular and Non Singular Operator

Singular and Non Singular Operator

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Unitary Operator

Unitary Operator

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

New Documents from this Course

Modulus Study Documents

Modulus Study Documents

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Synchronous Counter

Synchronous Counter

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Full-Subtractor Coursework Materials

Full-Subtractor Coursework Materials

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Multiplier - Academic Notes

Multiplier - Academic Notes

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Comparator - Educational Materials

Comparator - Educational Materials

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Ripple Carry Adder

Ripple Carry Adder

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

MUX (Multiplexer) - Study Materials

MUX (Multiplexer) - Study Materials

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Assignment 2: Q and A

Assignment 2: Q and A

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Answer Key

Sequential Circuit - Study Note

Sequential Circuit - Study Note

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Latch (Temporary Storage of Bits)

Latch (Temporary Storage of Bits)

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Set-Reset Flip-Flop

Set-Reset Flip-Flop

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note

Delay Flip Flop

Delay Flip Flop

Santa Fe College PHY 2048 | General Physics 1 with Calculus

Lecture Note