I have been trying to figure out something that should be quite basic. I have some data that describes the motion of an object when exposed to waves. Between the wave amplitude and the amplitude of the object's motion there will be a phase shift. This phase shift is defined as lead phase, i.e. lag phase when negative. When I try to convert the data to another coordinate system, the phase shift will be different. Does anyone know any rules that relates phase shifts to a coordinate system? It can also be noted that the data in the coordinate system that I have, is defined with a positive wave direction opposte of the other coordinate system.
Any help is appreciated!
Waves are graphed as trigonometric functions.
e.g. y = sin θ
A more general form of that would be y = a*sin (bθ + c), where a is the amplitude, b is the frequency and c is the phase shift. Hopefully that's the kind of thing you wanted.
Why did the vector cross the road?
It wanted to be normal.
The c should solve the equation at time zero. If your coordinate system is inverse to the data you should add pi to the previous c to change the sign of the position.
Thanks for your answers, however I am still a bit stuck. I'll try to give a more thorough description of the problem. In the attached picture two vessels, A and B, are illustrated. The blue vectors illustrate the waves and how their angles of attack are measured. When the waves hit the vessel, there will be motions in 6 degrees of freedom; surge, sway, heave, roll, pitch and yaw.
Surge=motion along x-axis
Sway=motion along y-axis
Heave=motion along z-axis
Roll=rotation about x-axis
Pitch=rotation about y-axis
Yaw=rotation about z-axis
The data I have is called RAO (response amplitude operator) data and is equal to the amplitude of the vessel motion (in meters or radians) divided with the amplitude of the waves. As mentioned, it is between these two amplitudes the phase shift will occur. My problem is that I can't seem to figure out how the phase shifts will change for the different degrees of freedom when the data is converted from B) to A).
Any clever minds have a clue?
I am thinking that you will not be able to use a single equation to give you all of those motions in three-dimentional space. For example, the formula that mathsyperson gave you is generally used to find the position of a particle within a wave. However, this relates to only movement along the y axis for a specific point in time.
My thinking is that all of your movements will correspond somehow to the frequency of the wave in question. I am leaning toward the necessity of creating a different wave function for each individual movement. This is because the amplitude (Or A of the original equation) will be different in magnitude as well as direction for these different yet connected parameters.
Also, just wondering, is the origin of these waves stationary or moving? If the origin moves all of your functions will become much more complicated also. Each function will have to change as the source and direction change.
I hope that you are getting paid for this endevour because it sounds like you will have to make a lot of relationships between a lot of variables to pull this off. Good luck pouring over that data.
I have not been on this site for long, but there may be a place to post such information. If there is I would like to try to model this motion. It seems like a worthy challenge. Sorry I could not help you more, but I would try to make a function that works along each axis first and then try to find a relationship among them. This way it won't be so daunting. In short, I do not believe that a particular phase shift will work to model this movement.
Thanks for a a well thought-through answer!
It seems I forgot to mention a couple of important factors that will simplify the problem. The coordinate system is attached to the vessel, and the origin is at the vessels centre of mass. Furthermore, you are correct in that the different frequencies will induce different movements, and that there are different functions for the different degrees of freedom. In the attached pic, you can see how this data looks, for one specific wave heading (0 deg., i.e. hitting directly on the stern in "B)" in previous pic).
For example in the data for a heading of 180deg (opposite direction) the phases will be negative for the surge motion, and it is this I am trying to figure out.
Hope this was of some help, and thanks again.
sorry, the pic didnt upload the first time as it was too big.
Poor Danster, not only do you have to create seperate functions for each axis but you also have to have a variable within all of those functions which changes them depending on the location of the source of the wave.
To make matters even worse the data suggest that you have to model a dampening force within these functions. This data will never correspond to the general wave equation that we have been talking about. My poor fellow you are going to have to do a lot of careful studying of the interaction between the forces interacting here. I wish you all of the best and I tip my hat to you for giving it a go.
Good luck and drop a line if you can think of anything else. I have an inkling that you will be working on this for a while unless you are extremely gifted in physics.