5
There are two parts to your question. The first part is how do you form the mass and stiffness matrices for a dynamic system. The second part is how do you solve the eigenvalue problem to get the natural frequencies and mode shapes. I will answer the the second part first and then the first part.
Solving eigenvalue problems for dynamic system.
I am going to ...
4
A more "Mathematica" way of generating your base states is via Tuples
states = Tuples[Range/@{2,3,2}]
To then get the independent pairings of states, you can use
pairs=Flatten[Table[states[[{i,j}]],{i,1,Length@states},{j,i,Length@states}],1];
{{{1, 1, 1}, {1, 1, 1}}, {{1, 1, 1}, {1, 1, 2}},
{{1, 1, 1}, {1, 2, 1}}, {{1, 1, 1}, {1, 2, 2}},
{{1, ...
3
Based on the suggestion of Henrik Schumacher, and the answers of Hausdorff and Daniel Huber, you can do it as follows:
Format[braket[{{a_, b_, c_}, {d_, e_, f_}}]] :=
Row[{"\[LeftAngleBracket]",
StringRiffle[{ToString[a], ToString[b], ToString[c]}], "|", "|",
StringRiffle[{ToString[d], ToString[e], ToString[f]}],
&...
1
Often a problem is easier, seen from another perspective.
You have different quantum states, specified by 3 integers. We may e.g. represent these as lists:
states=Flatten[Array[{#1, #2, #3} &, {3, 3, 3}], 2]
Now, you want bra-kets that are symmetrical, that is <a||b> and <b||a> are identified. Instetad of thinking in "bra-kets", ...
1
FWIW, my take on the big problem. I'm not particularly interested in parsing strings, so I can delete if this is unhelpful.
(*"
* Calculator
"*)
CellPrint@
ExpressionCell[
Manipulate[
Column[{
(* displays some data for inspection *)
Dynamic@{var, formula},
Dynamic@Quiet[
(* TBD:check input/output of Solve *)
...
1
Here's a quick and dirty version that I think should come close to what you're asking for. The handling of the variables and their localisation is not very sophisticated, but it should work for simple formulas:
Clear[a, b, c]
eq = c^2 == a^2 + b^2;
vars = Reduce`FreeVariables[eq]
sol = "";
Manipulate[
Evaluate@Column@{HoldForm[Evaluate@eq], eq, ...
1
Clear["Global`*"]
$Version
(* "12.3.1 for Mac OS X x86 (64-bit) (June 19, 2021)" *)
Enter equation to be used (equation must use Equal (==) rather than Set (=))
eqn = (Voltage == Current*Resistance);
vars = Variables[Level[eqn, {-1}]];
Manipulate[
Column[{
StringForm["Equation: ``", eqn], "",
Reduce[eqn, ...
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