Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
The state transition matrix has the following properties: 1) For every to stist₂ER, $(testo)=$(testi) 0 (tisto) eq(i) 2) For every to tER, § (t,to) $(tot)=I eg (2) 3 For every to, ter, d§ (t, td=-$(t,to) A (to) Jto Qu: Prove Eq (2) in above. (Using eq:3) eq(3)

The state transition matrix has the following properties: 1) For every to stist₂ER, $(testo)=$(testi) 0 (tisto) eq(i) 2) For every to tER, § (t,to) $(tot)=I eg (2) 3 For every to, ter, d§ (t, td=-$(t,to) A (to) Jto Qu: Prove Eq (2) in above. (Using eq:3) eq(3)

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
See similar textbooks
icon
Related questions
Question
The state transition matrix has the following properties: 1) For every to stist₂ER, $(testo)-0(testi) (tisto) eq(1) & 2) For every to tER, § (t, to) $(tg))=I eg(2) 3) For every to, tER, J (t₁t)- - § (t,t√) A (to) Jto Qu: Prove Eq (2) in above. (Using eq. 3) eq(3)
Transcribed Image Text:The state transition matrix has the following properties: 1) For every to stist₂ER, $(testo)-0(testi) (tisto) eq(1) & 2) For every to tER, § (t, to) $(tg))=I eg(2) 3) For every to, tER, J (t₁t)- - § (t,t√) A (to) Jto Qu: Prove Eq (2) in above. (Using eq. 3) eq(3)
Expert Solution
Step 1

Given:

A state transition matrix, Φ.

For every t0,t∈ℝ, ∂Φ∂t0t,t0=-Φt,t0At0.

 

To prove:

For every t0,t∈ℝ, Φt,t0Φt0,t=I.

 

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS