solving a deceptively simple-looking switched RC circuit (singular circuit ?)

Hi,

I am confronted with what I believe is a "singular circuit" and I am
having difficulty determining initial conditions for solving it ...


Here is a description (with links to figures):

A DC source first charges a -----C2-----(R1 || C1)----- circuit.  At
time t=T, two switches are thrown: one disconnecting the DC source, and
the other, connecting the "charged" portion of the circuit to a big
capacitor C3 (which may already have some charge on it).  The circuit
therefore becomes  (-----C2-----(R1||C1)-----) || C3.

I've posted a schematic of the circuit for t=<T- (before the switching)
here:
http://ca.pg.photos.yahoo.com/ph/enginquiry/detail?.dir=/c44b&.dnm=2fb4.jpg&.src=ph

At switch time t=T-, C1, C2, and C3 all have charge and the circuit has
not yet reached steady-state.

At time t=T+ (after switching), the circuit becomes:
http://ca.pg.photos.yahoo.com/ph/enginquiry/detail?.dir=/c44b&.dnm=3ce9.jpg&.src=ph

This is the circuit I want to solve.  The chief difficulty is that i
don't know what the initial conditions are for t=T+.  I cannot assume
that the voltages on the capacitors are continuous across t=T bacause I
am connecting capacitors in parallel at t=T. Charges will flow to
balance the voltage on the (-----C2-----(R1||C1)-----) network and the
C3 capacitor "instantaneously" (need to model this current with a delta
function).

If I could figure out the initial conditions, thenI would  solve the
resulting ciruict by replacing the charged-capacitors with a DC source
and an uncharge capacitor is series like this:
http://ca.pg.photos.yahoo.com/ph/enginquiry/detail?.dir=/c44b&.dnm=1641.jpg&.src=ph

I'd then solve by superposition ...

Any thoughts ?  Can anyone tell me how to calculate the initial
conditions on the capacitors at t=T+  ?  How do the charges
re-distribute on C1, C2 and C3 at t=T ?

Thanks,
Dan

.

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