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1. Navier-Stokes V 29 / ρ.p ρ.f - μ / (* g * R 2^* ≡

2. Setup the implicit expr expr 29 / ρ.p ρ.f - μ / (* g * R 2^* V - :

3. Solve for 'R' Optimiz: Symbolic expr R solve maple 3 ρ.p ρ.f - (g * V * μ * sqrt * g 2 sqrt * ρ.p ρ.f - (* / 3 ρ.p ρ.f - (g * V * μ * sqrt * g 2 sqrt * ρ.p ρ.f - (* / - 21 mat

ρ.p ρ.f 21 mat weight density particule [sphere] weight density fluid 21 mat ≡

Given/measured terminal velocity 'V', 
solve for viscosity 'μ' wrt: ρ => [p,f], 
R=>[radius of the sphere, droplet] expr μ solve maple 2 ρ.p ρ.f - (* g * R 2^* 9 V * /

29 / ρ.p ρ.f - μ / (* g * R 2^* V ≡ μ solve maple 2 ρ.p ρ.f - (* g * R 2^* 9 V * /

Maple classical/direct inverser

x a b q 1 x b / - exp (a^- :

x a b q y ≡ x solve maple 1 y - ln b * a / -

y a b sol 1 y - ln b * a / - :

a 2 : b 0.5 : 12 mat

x middle x :

x a b q x a b sol x middle 3 1 sys

Lambert W, principal branch

Lambert W is not a function: it is a "solution function". Don't scratch your head looking for it, you won't find. In other words: it is not a built-in aprroximation. You can fake a built-in like here in Smath. There is the good approximation "ProductLog" from Mathsoft Collaboratory.

<= solve ..... Compare Lambert ..... => roots

y W x x exp * y - 0 ≡ x 1 e / - e solve :

x Lambert w w exp * x - 0 ≡ w 0 roots :

Lambert W [solve conventional]

x W 1 e / - 1 1 e / - 1 - 2 2 mat 2 1 sys

Lambert [roots conventional]

x Lambert 1 e / - 1 1 e / - 1 - 2 2 mat 2 1 sys

x ProductLog e 1 exp : u x e > x ln x ln ln - x 1 e / + sqrt 1 e / sqrt - if 11 line : w 2 u * : u w - abs u abs / 1010 -^> w u : u u 2^x e u -^* + 1 u + / eval : 21 line while 31 line u 31 line :

x Lam x ProductLog eval :

x ProductLog 15 decimals ≡

Plot eval(,,) Lambert W(x)

x Lam

1 Lambert 0.567143290409783

1 W 0.567143289179478

W1 Neil_Sloane (0.5671432904097838729999686622 ≡

1 ProductLog 0.567143290409783

Two dead horses doing right

expr x x exp * y - :

y LambertW expr y solve maple :

x LambertW

The centered XY system x y XY x y + y / (2 x y / * 1 + (- :

y x L x x exp * y - :

L XY 2 1 sys

The section below will work on Smath versions that have the f(x) menu "FindRoots" It was created with Smath 5346 UNofficial release.

Create the meaningful multivar solver # # GivenFind f init FindRoot (:

Solving a user system ===================

f a0 0 ≡ a1 c ≡ a1 a2 + a3 + 0 ≡ a1 2 a2 * + 3 a3 * + b ≡ 41 mat :

init a0 1 ≡ a1 1 ≡ a2 1 ≡ a3 1 ≡ 41 mat :

b 1 : c π : 21 line

k1 10.052 : k2 14.836 : k3 4.982 : 13 mat

f γ1 γ2 + k1 k2 + k3 + ≡ γ1 γ2 * k1 k2 * k1 k3 * + ≡ 21 mat :

init γ1 0 ≡ γ2 0 ≡ 21 mat :

a0 a1 a2 a3 sol f init GivenFind :

f init GivenFind #

a0 a1 a2 a3 sol #

Solving the line-circle system ==========

C 6 : Circle ≡

L 0 : Line ≡

Φ vector equalities f C x 2^y 2^+ ≡ L x y + ≡ 21 mat :

init x 1 ≡ y 1 ≡ 21 mat :

Does not support assignment f init GivenFind #

x y find f init GivenFind :

Solving quaternion ================

x y find #

α 0.5 :

β 1.5 :

The Quaternion system f p q + r - 0 ≡ p 2^q 2^+ r 2^+ 1 ≡ β p * α r * + 0 ≡ 31 mat :

C x 2 ^ - sqrt C x 2 ^ - sqrt - L x - 3 1 sys

init p 0 ≡ q 0 ≡ r 0 ≡ 31 mat :

Sanity check vs Mathcad 11 f init GivenFind #

p q r find f init GivenFind :

p q r find #

Sanity check vs Mathcad 11 f init FindRoot #

p q r 31 mat #