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Re: NDSolve and hybrid dynamics (Differential Algebraic Equation DAE)
*To*: mathgroup at smc.vnet.net
*Subject*: [mg113553] Re: NDSolve and hybrid dynamics (Differential Algebraic Equation DAE)
*From*: Bob Hanlon <hanlonr at cox.net>
*Date*: Tue, 2 Nov 2010 05:02:17 -0500 (EST)
If is a programming construct not a mathematical function. Use Piecewise
eqns = {x'[t] == y[t] + Sin[t],
y[t] == Piecewise[{{1, t < 1/10}}, 2],
x[-Pi] == 1/2};
sol = {x[t], y[t]} /. DSolve[eqns, {x[t], y[t]}, t][[1]]
{(1/2)*(-1 + 2*Pi + 2*Piecewise[{{t - Cos[t], t <= 1/10}},
-(1/10) + 2*t - Cos[t]]), Piecewise[{{1, t < 1/10}}, 2]}
Plot[sol, {t, -5, 1},
Frame -> True,
Axes -> False,
Exclusions -> 1/10,
ExclusionsStyle -> Red]
For NDSolve break the problem into two regions
Bob Hanlon
---- Ravi Balasubramanian <ravi.balasubramanian at yale.edu> wrote:
=============
Friends,
I am trying to solve a hybrid dynamics problem using NDSolve.
I am aware that I could use the event locator methods in NDSolve and
manually take care of the transitions (set initial conditions etc). But
my system is complicated, and I would have to do a lot of book-keeping.
The following represents a simplified version of the problem.
eqns = {x'[t] == y[t] + Sin[t], y[t] == If[t < 0.1, 1, 2],
x[-Pi] == 1/2};
sol = NDSolve[eqns, {x[t], y[t]}, {t, -5, 5}]
It is a first order differential equation in x[t], but it includes a
y[t] variable that is discontinuous. There should be solution for this
problem, but I get the following error message from NDSolve.
LinearSolve::"nosol" : "Linear equation encountered that has no solution.
The error is probably arising from the "If" condition.
FYI, in my real system the y[t] variable is a Lagrange multiplier that
is enforcing a constraint. Under certain conditions, that constraint is
broken and the system transitions into another state. It will be great
if this problem can be solved with NDSolve keeping track of the y[t]
variable for me. Any suggestions greatly appreciated.
Thanks!
Ravi Balasubramanian
Yale University
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