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2.7 Given that the spacial components of motion, x = x(X, (), are: x₁ = X₁ + X₂ (e' - K), X₂X₁ (e¹-K) + X₂ x3 = X3, show that the material components of motion X = X(x, t), are: X₁ = [-x₁ + x₂(e¹-K)] / [K(K-e' - e ¹)] X₂=[x₁(e¹-K)-₂]/[K(K-e²e^¹)] X3 = x3

2.7 Given that the spacial components of motion, x = x(X, (), are: x₁ = X₁ + X₂ (e' - K), X₂X₁ (e¹-K) + X₂ x3 = X3, show that the material components of motion X = X(x, t), are: X₁ = [-x₁ + x₂(e¹-K)] / [K(K-e' - e ¹)] X₂=[x₁(e¹-K)-₂]/[K(K-e²e^¹)] X3 = x3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2.7 Given that the spacial components of motion, x = x(X, (), are: x₁ = X₁ + X₂ (e' - K), X₂X₁ (e¹-K) + X₂ x3 = X3, show that the material components of motion X = X(x, t), are: X₁ = [-x₁ + x₂(e¹-K)] / [K(K-e¹'-e'')] X₂= [x₂(e¹-K) -₂]/[K(K-e¹-e¯')] X3 = x3
Transcribed Image Text:2.7 Given that the spacial components of motion, x = x(X, (), are: x₁ = X₁ + X₂ (e' - K), X₂X₁ (e¹-K) + X₂ x3 = X3, show that the material components of motion X = X(x, t), are: X₁ = [-x₁ + x₂(e¹-K)] / [K(K-e¹'-e'')] X₂= [x₂(e¹-K) -₂]/[K(K-e¹-e¯')] X3 = x3
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