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mgt1 j + p1 = mgt2 j + p2 (vector p's) [1]
This is formally similar to the conservation of energy equation,
the
difference being that it is a vector equation and that it involves
momentum and a term mgt analogous to mgy. The energy equation
conserves the sum of KE and a positional energy. The other equation
conserves the sum of momentum and a temporal term.
Is anyone aware of an attempt to develop a momentum-time conservation
approach
to physics similar to the familiar KE-position conservation
approach - i.e., an attempt to avoid an impulse-momentum approach by
using a conservation law involving momentum and a temporal potential
of sorts similar to an avoidance of a work-KE approach by using
conservation of KE and positional energies? I would assume that the
biggest impediment would be finding suitable forces that are
functions of time instead of position.
Conservation of Energy (a scalar conservation law) and Conservation
of Momentum (a vector conservation law) are true under different
conditions. It is possible for either, both or neither to be true
depending upon the conditions.
Noone in this thread is denegrating the usefulness of the momentum
conservation theorem for closed systems.
We were speculating regarding the possible usefulness of defining a
"potential momentum function" and turning the impulse/momentum theorem into
a conservation principle encompassing external forces.