PHY.6:4.4 - Connect the physical relations before choosing a solving order

State what a connection makes common and what it transfers. Match quantities, units, frames and orientations at that connection. Equal values require a physical reason: two locations in contact can still have a finite resistance or an intervening store. If the connection has its own consequential dynamics, describe those dynamics.

Combine the part balances through the common transfer. Transfers internal to the combined boundary cancel when they describe the same exchange over the same interval. Retain conversions between quantities and energy forms. For an energetic connection, derive its power expression from the physical variables; variable names such as potential and flow alone do not establish their product as power.

Keep the equations as simultaneous relations while constructing the physical account. They can include derivatives, algebraic constraints, spatial dependence or statistical response. In a differential-algebraic description, some relations constrain values while others describe change. Which variable is solved for is a later mathematical or computational choice; changing that order need not change the physical interaction.

Eliminate a variable only while retaining the relation or reconstruction needed by later use. MMP.9 supplies mathematical reduction and MMP.10 supplies a formulation for the chosen analysis. If two parts disagree at their connection, return to their quantity meanings and physical assumptions before changing a solver.