Consider a piece of ground, or a spot in a building. When there is an earthquake, this lump starts to move. We can describe its particle motion in 3D if we can measure three components, up-down, north-south, and east-west. Much like the tree in the forest, this motion can only exist for us if we measure it. We do that using an instrument which measures the acceleration on the 3 components.
Acceleration doesn't tell us how it is moving, but if we have a total history of acceleration from time=0, we can integrate once to get velocity (yeah!), or integrate twice to get displacement. Then with a fancy computer program we can get a little movie on how it moved during the earthquake. The double integration is a mathematical bitch, and sometimes it is better to measure the displacement directly, such as with gps.
Has the motion of this instrumented lump been completely described? NO! There's a matter of the 3 rotational components.
Here we have our 3 components. If the lump is at the centre, and you grabbed each axis and gave it a twist, that would describe the rotational components. Here's the complexity. Although I could have a movie of that little lump moving around this axis system, the rotational components would have to follow the lump. A whirling lump makes for a very complex movie. That's why most rational people forget about all this.But thank goodness there are people who care about this arcane aspect of particle motion! The first people were those who are tryng to measure gravity waves. Old Einstein threw out a teaser when he said that when two huge objects, such as black holes, start to dance with each other, they will throw out gravity waves which propagate at the speed of light. Ever since, there have been crazies ;) trying to measure these things. No luck yet.
-to be continued, as usual, after I count my pennies. :)
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