# Model Mathematics

### Component: Py

$ddtime Py = r4 ⁢ Py1 - r3 ⁢ Zn 2 ⁢ Py$

### Component: Py1

$ddtime Py1 = r3 ⁢ Zn 2 ⁢ Py + k_1 ⁢ Qw2 - r4 ⁢ Py1 + k1a ⁢ Dw ⁢ Py1$

### Component: Dw

$ddtime Dw = k_1 ⁢ Qw2 + k3 ⁢ Qw1 + k_2 ⁢ Qw1 - k1a ⁢ Dw ⁢ Py1 + k2 ⁢ Dw ⁢ Rw$

### Component: Rw

$ddtime Rw = k3 ⁢ Qw1 + k_2 ⁢ Qw1 - k2 ⁢ Dw ⁢ Rw$

### Component: Qw1

$ddtime Qw1 = k2 ⁢ Dw ⁢ Rw - k3 ⁢ Qw1 + k_2 ⁢ Qw1$

### Component: Qw2

$ddtime Qw2 = k1a ⁢ Dw ⁢ Py1 - k_1 ⁢ Qw2$

### Component: Mw

$ddtime Mw = k3 ⁢ Qw1$

### Component: Px

$ddtime Px = r2 ⁢ Px1 + k_1 ⁢ Qz4 - r1 ⁢ Zn ⁢ Px + k1b ⁢ Dz ⁢ Px$

### Component: Px1

$ddtime Px1 = r1 ⁢ Zn ⁢ Px + k_1 ⁢ Qz2 - r2 ⁢ Px1 + k1 ⁢ Dz ⁢ Px1$

### Component: Tp

$ddtime Tp = r6 ⁢ Tp1 - r5 ⁢ Zn ⁢ Tp$

### Component: Tp1

$ddtime Tp1 = r5 ⁢ Zn ⁢ Tp - r6 ⁢ Tp1$

### Component: Zn

$ddtime Zn = r2 ⁢ Px1 + r6 ⁢ Tp1 - r1 ⁢ Zn ⁢ Px + r5 ⁢ Zn ⁢ Tp$

### Component: Dz

$ddtime Dz = k_1 ⁢ Qz2 + k3 ⁢ Qz1 + k_2 ⁢ Qz1 + k_1 ⁢ Qz4 - k1b ⁢ Dz ⁢ Px + k1 ⁢ Dz ⁢ Px1 + k2a ⁢ Dz ⁢ Rz$

### Component: Rz

$ddtime Rz = k3 ⁢ Qz1 + k_2 ⁢ Qz1 + k3 ⁢ Qz3 + k_2 ⁢ Qz3 + k3 ⁢ Qz5 + k_2 ⁢ Qz5 - k2a ⁢ Dz ⁢ Rz + k2b ⁢ Qz4 ⁢ Rz + k2c ⁢ Qz2 ⁢ Rz$

### Component: Qz1

$ddtime Qz1 = k2a ⁢ Dz ⁢ Rz - k3 ⁢ Qz1 + k_2 ⁢ Qz1$

### Component: Qz2

$ddtime Qz2 = k1 ⁢ Dz ⁢ Px1 + k3 ⁢ Qz3 + k_2 ⁢ Qz3 - k_1 ⁢ Qz2 + k2c ⁢ Qz2 ⁢ Rz$

### Component: Qz3

$ddtime Qz3 = k2c ⁢ Qz2 ⁢ Rz - k3 ⁢ Qz3 + k_2 ⁢ Qz3$

### Component: Qz4

$ddtime Qz4 = k1b ⁢ Dz ⁢ Px + k3 ⁢ Qz5 + k_2 ⁢ Qz5 - k_1 ⁢ Qz4 + k2b ⁢ Qz4 ⁢ Rz$

### Component: Qz5

$ddtime Qz5 = k2b ⁢ Qz4 ⁢ Rz - k3 ⁢ Qz5 + k_2 ⁢ Qz5$

### Component: Mz

$ddtime Mz = k3 ⁢ Qz1 + k3 ⁢ Qz3 + k3 ⁢ Qz5$

### Component: model_parameters

$k3 = 0.0 if time ≥ 0.0 ∧ time < td0 0.011 if time ≥ td0 ∧ time < td$
Source
Derived from workspace Cui, Kaandorp, Lloyd, 2008 at changeset edffca194968.
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