Q5P Write the tensor transformation ... [FREE SOLUTION]

Chapter 10: Q5P (page 517)

Write the tensor transformation equations for $蔚_{i j k} 蔚_{m n p}$ to show that this is a (rank 6) tensor (nota pseudo tensor). Hint:Write (6.1) for each $蔚$ and multiply them, being careful not to re-use a pair of summation indices.

Short Answer

Expert verified

The tensor transformation equation for

${蔚^{'}}_{伪尾纬} {蔚^{'}}_{味 n 胃} = {(d e t A)}^{2} a_{伪 i} 伪_{尾 j} a_{纬 k} a_{味 m} a_{n m} a_{胃 p} 蔚_{i j k} 蔚_{m n p} = a_{伪 i} 伪_{尾 j} a_{纬 k} a_{味 m} a_{n m} a_{胃 p} 蔚_{i j k} 蔚_{m n p}$ .

Step by step solution

Given information.

Matrix definitions are given.

Definition of a rotation matrix.

The rotation matrix is defined in this way.

$[\begin{matrix} \cos 蠒 & - \sin 蠒 \\ \sin 蠒 & \cos 蠒 \end{matrix}]$

Define an orthogonal transformation.

It A is an orthogonal matrix, that defines an orthogonal transformation.

${蔚^{'}}_{伪尾纬} = (d e t A) a_{伪 i} 伪_{尾 j} a_{纬 k} 蔚_{i j k}$

Using the information $A = 卤 1$ make further simplifications.

${蔚^{'}}_{伪尾纬} {蔚^{'}}_{味 n 胃} = {(d e t A)}^{2} a_{伪 i} 伪_{尾 j} a_{纬 k} a_{味 m} a_{n m} a_{胃 p} 蔚_{i j k} 蔚_{m n p} = a_{伪 i} 伪_{尾 j} a_{纬 k} a_{味 m} a_{n m} a_{胃 p} 蔚_{i j k} 蔚_{m n p}$

Hence, the tensor transformation equation is shown below:

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91影视

Write the tensor transformation equations for $蔚_{i j k} 蔚_{m n p}$ to show that this is a (rank 6) tensor (nota pseudo tensor). Hint:Write (6.1) for each $蔚$ and multiply them, being careful not to re-use a pair of summation indices.

Short Answer

Step by step solution

Given information.

Definition of a rotation matrix.

Define an orthogonal transformation.

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Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity

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91影视

Write the tensor transformation equations for 蔚ijk蔚mnpto show that this is a (rank 6) tensor (nota pseudo tensor). Hint:Write (6.1) for each蔚and multiply them, being careful not to re-use a pair of summation indices.

Short Answer

Step by step solution

Given information.

Definition of a rotation matrix.

Define an orthogonal transformation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electricity

Thermodynamics

Famous Physicists

Work Energy and Power

Rotational Dynamics

Fundamentals of Physics

Study anywhere. Anytime. Across all devices.

Write the tensor transformation equations for $蔚_{i j k} 蔚_{m n p}$ to show that this is a (rank 6) tensor (nota pseudo tensor). Hint:Write (6.1) for each $蔚$ and multiply them, being careful not to re-use a pair of summation indices.