2011-04-04, 06:59 AM
If a force is variable, then the acceleration is also variable. Why should it "stop" after acceleration? The only reason that acceleration is considered the stopping point is that Newton's second law states F = m*a, but that doesn't mean that x'''(t), or any further derivatives don't exist.
Also, acceleration and any of its derivatives exist in R^3, so I don't see what you're trying to say here with your "higher dimensions". And by the way, increasing the number of dimensions isn't difficult a difficult task. Simply assign a scalar value (temperature, energy, luminance, time, etc.) to every point in space. The more variables assigned, the more dimensions. That also means that each derivative can be assigned to a dimension, but what's the point of doing this? It's not a true Cartesian coordinate.
Also, acceleration and any of its derivatives exist in R^3, so I don't see what you're trying to say here with your "higher dimensions". And by the way, increasing the number of dimensions isn't difficult a difficult task. Simply assign a scalar value (temperature, energy, luminance, time, etc.) to every point in space. The more variables assigned, the more dimensions. That also means that each derivative can be assigned to a dimension, but what's the point of doing this? It's not a true Cartesian coordinate.