chapter  9
Lorenz Equations
WithMitchal Dichter
Pages 34

9.1.1

The moment of inertia of a ring is the mass times radius squared. I water   =   M r 2

The rate of change of water is the rate at which water flows in minus the rate at which water flows out. M ˙   =   Q total − K M

First, we make a differential equation for I water I ˙ water   =   M ˙   r 2   =   Q total   r 2 − K   M   r 2   =   Q total   r 2 − K I

which has solution I water ( t )   =   ( I water ( 0 ) − Q   r 2 K ) e − K t + Q   r 2 K           lim t → ∞   I water ( t )   =   Q   r 2 K