[a B]T described by the following differentialConsider a system with input u and output y =equations:ä + 2BB + 4å + sin 3B + 582 + å cos a + sin B0) and find a linear state spacepart 1 Linearize the system about the operating point (B = 0, B = 0, arepresentation of the system.Part 2Find the state space representation of the system in controllable canonical form.

Given differential equations: α¨+2ββ˙+4α˙+sinβ=0β¨+5β2+α˙cosα+sinβ=u (a) We have to linearize the…

Answered: Consider a system with input u and…

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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Find the Product Solution of the PDE Uxx=U; U=U1(x+y) Seperate the PDE into System of ODES Uxx=Ut-U; U = U(X₁t)
Show that the 3D system x' = Ax is conjugate to the system x' = -x where a < 0 and A is given by а 1 0 A = 0 a 1 0 0 a
Express the given system of higher-order differential equations as a matrix system in normal form. x" + 6x+y=0 y" -2x=0 Which of the following sets of definitions allows the given system to be written as an equivalent system in no A. x1 = x', x2 =x", x3 = y', x4 = y" Question Viewer only the new variables? 'B. ×₁ = x, x₂ = x², x3 = y, x4 = y' C. x1 = x, x2 =x", x3 = y, x4 = y' D. X₁ =x', x2 = y' Write the system of equations using matrix notation. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) X1 X1 ○ A. x2 ×2 ○ ×1 ' X1 x2 N B. x2 ' X3 ха II x3 Ха
The system of non-linear differential equations x = -sin x COS Y, y = sin x + sin y, has an equilibrium point at (,0). (a) Calculate the Jacobian matrix of this system of equations and evaluate this matrix at the given equilibrium point. (b) Use your answer to part (a) to classify this equilibrium point.
Express the given system of higher-order differential equations as a matrix system in normal form. x"' + 3x+6y=0 y" - 5x=0 Which of the following sets of definitions allows the given system to be written as an equivalent system in normal form using only the new variables? O A. X₁ X₁ X₂=X", X₂ =Y₁X₂ =y" OB. X₁ X¹, X₂=X", X₂ = Y', X₂=y" OC. X₁ = x¹, x₂ = y' O D. X₁ =X, X₂=X', X3 = Y, X4 = Y' Write the system of equations using matrix notation. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) O A. co Xq' X₂ m A 11 II X₁ X₂ X3 X4
Suppose faN such that f is not onto but f+9 is onto Prove that 9 is onto or give a counterY example (use mapping for explain) N and :N-N are functions
Consider the system of equations. Edit 6. x' = 10 Find a fundamental matrix for the given system of equations. 2 ešt |-2 et V (t) = est Find the fundamental matrix (t) satisfying (0) = I. 2 ežt 0. (t) = 2 | 5 15
Express the given system of higher-order differential equations as a matrix system in normal form. x" + 5x+6y=0 y" - 5x=0 Which of the following sets of definitions allows the given system to be written as an equivalent system in normal form using only the new variables? O A. x₁ = x¹, x₂ =y' O B. X₁ =X, X₂=X', X3 = Y, X4=y' OC. x₁ = x, X₂=x", X3 = Y. X4=y" OD. x₁ = x¹, x₂ = x¹, x₂ =y', X4=y" Write the system of equations using matrix notation. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) O A. O B. X₁ X₂ x₁² X1 x2 x3 X4 X1
Describe any one of the physical systems where we can apply Legendre or Bessel differential equations.
Exercise: Solve the following system x'=y +1 y'=x +1 (a)] (b)
Show your work
For the system of differential equations, X1, X2 a) Find the characteristic polynomial of the matrix of coefficients A. CA(X) b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order separated by commas. U₁ = U2 = = y' = c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller eigenvalue X₁ and u2 is the eigenvector associated with the larger eigenvalue A2. 5 2 - 1 Y2 (t) d) Determine two linearly independent solutions to the system. Enter the first solution in the format y₁ (t) y = = y₁ (t) Enter the second solution in the format y₂(t) = ƒ2(t) (v3h₁(t) + v₁h₂(t)) = : fi(t) (vigi(t) – v2g2(t)) . +

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