Studying a nonlinear system under constraints in linear fashionby dotiozeros Tags: dynamical system, linear algebra 

#1
Dec3112, 04:20 AM

P: 1

Suppose that [itex]a = aBc[/itex] where [itex]a[/itex] and [itex]c[/itex] are vectors and [itex]B[/itex] is some matrix that changes as time "continuously" goes on  making this system dynamical system. But suppose that at any time, if [itex]B[/itex] is linearized into square matrix, it is proven that it is impossible to satisfy [itex]a = aBc[/itex]. Does this mean that in nonlinear case, there would not be any case that satisfies [itex]a = aBc[/itex]? Also, if nonlinear case allows satisfying the equation, what would be the condition? If the latter question is somehow ambiguous, answer to the first question is fine.
Caution: [itex]a[/itex] is transposed form of a vector. About [itex]a[/itex] and [itex]c[/itex]  what happens if we separate the case into two  one that has [itex]a[/itex] and [itex]c[/itex] change as time goes on(which means [itex]B[/itex] changes) and one that has these two fixed? 


Register to reply 
Related Discussions  
fist and second order constraints in a system?  Classical Physics  2  
Nonlinear Dynamics: Nullclines and phase plane of a nonlinear system  Calculus & Beyond Homework  1  
Linear & nonlinear shooting and linear & nonlinear finite difference methods  Calculus & Beyond Homework  0  
Is marginal constraints equivalent to linear constraints?  Set Theory, Logic, Probability, Statistics  1  
numerical solutions of system of nonlinear algebraic equations nonlinear algebraic eq  General Math  6 