Initializing a system of abstract functions with a for loop [closed]

Question

I am trying to initialize a collection of abstract functions $\theta_k(t)$ in a variable $t$ where $1\leq k\leq n$.

I cannot define them explicitely; the entire point is that I want to numerically solve an ODE I can define with their derivatives. It's clear how I can do this if I had the array, but I don't know how to initialize the array.

If I only cared about a particular value for $n$, I could declare an array of functions explicitly like this:

thetas = Array[{theta1[t_], theta2[t_], ... , thetan[t_]}]

There should be a away to initialize an array of abstract functions in the variable $t$. Once I have such an array, thetas, I can likewise initialize a second array, derivs such that

For[i=0,i<n, ++i,
derivs[[i]]=Sum[matrix[[i,j]]Sin[Abs[thetas[[j]]-thetas[[i]]]],{j,0,n}]
]

and then use NDSolve as suggested in the comments:

NDSolve[derivs, thetas[0] = myInitialCondition, thetas, {t,0,reallyBigNumber}]

Answer 1

Looks with With could be used.

a way to initialize an array of abstract functions

With[{vars = Array[theta, 3]}, vars = {"a", "b", "c"}]

or with non-ordinal indices

With[{vars = {theta[4], theta[7], theta[8]}}, vars = {"a", "b", "c"}]

e.g.

theta[8]

c