<p> Quaternion stuff + Breather </p>

e5a382b0-4932-4acd-8441-74066b57a35d 26 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

a 0.5 :

β 1.5 :

# # Solve

Solve("1:expression", "2:expression") - [Maxima] Solve(eqn, var) solves eqn for var. eqn is a boolean equation or a list of equations, var is a variable name or a list of names to solve for. Returns solutions as boolean equations var=value. Multiple solutions are given as a row vector. Use Assign() in order to apply solutions as assignments to var.

Solving this typical Quaternion system is NOT resident in the downloaded SmathStudio 2014_11_16 Maxima 5_34_1. So, you will be "zap" for this one in your work sheet.

C:\Smath+Maxima\2014 11 16 SMath and Maxima\Maxima-5.34.1\bin\maxima.bat

α 0.5 :

β 1 :

p 0.2 :

<p> Quaternion stuff + Breather </p>

1. Given the Quaternion vector system, it has two orthogonal vector solution, of which the symbolic expansion is 'V'.

2. Define some constant term "modulo"

modulo 2 β 2^* 2 β * α * + 2 α 2^* + sqrt :

V β - modulo / β modulo / β α + (modulo / β α + (- modulo / α modulo / α - modulo / 32 mat :

V 0.5345 - 0.5345 0.8018 0.8018 - 0.2673 0.2673 - 32 mat

3. Create the Quaternion vector

q V 1 col p stack :

q 0.5345 - 0.8018 0.2673 0.2 41 mat

4. Define the "UnitV", apply to 'q'

# norme Euclidean norm ≡

q q q norme / :

q that goes in 'quat' converter

q 0.5241 - 0.7862 0.2621 0.1961 41 mat

5. The rotation 'quat' converter

quat 12 q 3 el (2^* - 2 q 4 el (2^* - 2 q 2 el * q 3 el * 2 q 1 el * q 4 el * - 2 q 1 el * q 3 el * 2 q 2 el * q 4 el * + 2 q 1 el * q 4 el * 2 q 2 el * q 3 el * + 12 q 2 el (2^* - 2 q 4 el (2^* - 2 q 1 el * q 2 el * - 2 q 3 el * q 4 el * + 2 q 1 el * q 3 el * - 2 q 4 el * q 2 el * + 2 q 1 el * q 2 el * 2 q 3 el * q 4 el * + 12 q 2 el (2^* - 2 q 3 el (2^* - 33 mat :

γ quat :

ρ 1 b 2^- :

b 0.4 :

w ρ sqrt :

ρ 0.84

u v d b w b u * cosh (2^* b w v * sin * (2^+ (* :

u v f u - 2 ρ * b u * cosh * b u * sinh * u v d / + 2 w * b u * cosh * w v cos * w v * cos * - v sin w v * sin * - (* u v d / 2 w * b u * cosh * w v sin * w v * cos * - v cos w v * sin * - (* u v d / 31 mat :

M u v f 13.2 - 13.2 37.4 - 37.4 2020 CreateMesh :

If you want a nice view of fixed rotation <= disable ... enable =>

γ 0.7857 0.6177 0.0337 0.2065 0.3132 - 0.927 0.5831 0.7214 - 0.3736 - 33 mat

γ 0.5 0.5128 0.0131 - 0.5128 - 0.5 0.0128 0.0131 0.0128 133 mat :

zoom 0.875 :

M t f t B M zoom * γ * eval : t B 1 col t B 2 col augment 21 line :

step1 00 range :

c 00 + 200 red 15 mat :

Figure 44 - Breather 14 black 15 mat :

Quaternion rotation

M t f c Figure 3 1 sys

The 3D solid Breather will produce few Quaternion rotation that will not hurt the eyes. The combined Quaternion is very reactive and Breather explodes easily ... α= 0.5, β= 1, p= 0.2 are acceptable. Euler rotation of Breather is more manageable.

Some nice Breather from Mathcad 11 Quaternion, meshed 199 x 199 Would be great if Smath could render something like GNU plot Kuen surface example. As it looks from work sheet above, Smath does not access Maxima 3D plot ?