dE_logics said:
From what I think, any physical value has at most 3 parts -
1)Orientation - Or more explicitly, the angle that it makes with axis of the Cartesian coordinate system. Transforming will not change this value.
2) Position - This is the translational stuff...exactly from which point to which point.
3)Direction, after defining orientation and position, the line drawn (representing the physical value) should also have a direction at which it points. Since the orientation and position has been defined, there are only 2 values for this.
I don't think the position is specific, but however, if I'm right then what does a scalar and vector define?
If you are talking about a physical entity in space, you are almost correct. Orientation and direction can be seen as the same thing. Essentially the orientation refers to how something is "pointing" and in which direction. One way we can calculate orientation is to use an axis-angle formation. Another way is to use Euler angles. Another way is to use a quaternion. All ways are equivalent to representing orientations.
When we talk about orientation we have to take into account the dimension of time. In einsteins theory of relativity we have an extra dimension for time. Now we must note that this is relative and in this way there is no real accepted global definition of time. If we however integrate quantum mechanics into the structure space-time we can come up with a globalized picture of time however I won't get into this.
For simple purposes let's assume that we have the concept of absolute time as Newton noted. This approximates reality and its good enough for things at low speeds.
In this model we can represent orientation with one of the things I mentioned above. Either
* A Quaternion, or
* Euler Angles, or
* Axis-Angle formation with rotation angle
will suffice. I recommend learning quaternions when thinking about orientation as they have some very nice properties akin to matrix algebra. Ken Shoemake wrote a good book on quaternions in computer simulation and this sort of thing applies to describing orientations in the real world. You can also read Hamiltons original treatise on quaternions which I highly recommend (and its free! Search for Treatise Quaternion Hamilton on google)
Position is just a vector in some space. We have different types of spaces like for example cylindrical, spherical, cartesian, and others that are defined with a vector with the number of dimensions (in this case 3 in our Newtonian universe).
Now the best way to think of this is to think that we want to have a global spatial structure. Let's use the cartesian structure of space (ie orthogonal axis each 90 degrees
of relative angular measure apart) as the structure in which all space will act. We can convert between the different spaces using an appropriate transform.
The first definition is the typical definition of orientation. For example we can have a three dimensional object that is in three dimensional space. The first two angles give the direction that the object is facing. The third angle gives an angle that rotates about this axis (Hence the reference to angle-axis).
We can view this in two ways. First take a camera point it in a direction and then rotate it
about that axis in so many radians and you get the "orientation" of that camera. We can also
do the same thing to a plane and we get the same sort of result.
To represent the orientation and position we require a minimum of six elements (three angles and a position vector of three elements in a Newtonian universe). This will represent any objects direction, orientation, and position accurately.
A scalar is just a one dimensional vector. A vector is a generalized concept in that the vector generalizes the number of dimensions in some given space. There is a whole theory to vectors, vector spaces, and the appropriate laws of algebra for vectors and systems of vectors but that is beyond this post (I don't have time to explain it). I recommend you read a book about trigonometry to understand the basic ideas for cartesian spaces and read a thorough book on algebra (not something that just places the identities there but something that derives the identities) to have a good grasp of why the algebra works the way it works.
I wish you all the best.
