Custom Head for Encapsulation

Question

Often when I'm writing a project in Mathematica, the number of arguments I must provide to functions spins out of control.

I need a sort of object-oriented encapsulation approach. I've already had a go at doing this in Java, and now believe than an object-oriented language is not well suited to my needs.

Example:

Here I fetch data for the geodesic of a test particle in a pseudo-Riemannian manifold. The user must supply the metric in matrix form, the initial positions and velocities, and other miscellaneous things:

NGeodesicData[( {
    {(1 - (1/#2)) &, 0 &, 0 &},
    {0 &, -(1 - 1/#2)^-1 &, 0 &},       (*Matrix of real functions*)
    {0 &, 0 &, (-#2^2) &}
   } ) , 
    {{0, 50, 0.}, {Null, 0., .0008}},   (*Initial position and velocity*)
    {1, True, True},                    (*Miscellaneous*)
  2500, .01, 1]                         (*Numerical integration settings*)

All of these arguments are necessary, and I would like to structure them in a more manageable format.

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Specifically, I would like a head called TangentVector which consists of:

1. An n x n matrix of real functions of n variables each. (The matrix of real functions)
2. A list of two n-dimensional vectors. (the initial position and velocity; a tangent vector)

I am used to object-oriented languages where I can program a constructor in which I can perform checks, throw exceptions or warnings if I need to, and store a couple of fields based on the input. Basically, I'm looking to do the same thing here.

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How can I create such a TangentVector structure, and make a constructor for it?

I believe I have already found a solution to complicated pattern-matching (on the inputs to the constructor) here.