By Andy Ruina, Rudra Pratap
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Extra resources for Introduction to Statics and Dynamics
Definition of force. First, the relation between force and deformation gives us a definition of force. Force can be defined by the amount of spring stretch it causes. Thus most modern force measurement devices measure force indirectly by measuring the deformation it causes in a calibrated spring of some kind. That force can be defined in terms of deformation is one justification for calling ‘mechanical behavior’ the first pillar. It gives us a notion of force even before we introduce the laws of mechanics.
6 Cross product as a matrix multiply . . . . 4 Moment . . . . . . . . . . . . . . 5 Solving vector equations . . . . . . . . . . 8 The rules of vector algebra. . . . . . 10 Existence, uniqueness, and geometry . . . 38 ✌ Introduction to Statics and Dynamics, c Andy Ruina and Rudra Pratap 1992-2009. 40 . 41 . 42 . 58 . 58 . 63 . 67 . 68 . 73 . 74 . 83 . 92 . 93 . 95 . 6 Equivalent force systems . . . . . . . . . . 11 means add . . . . . .
3. The heirarchy of models We will rate this as a ‘good model’ if the damage to the plastic mimics the damage to a real car. This is expressed by the success at ‘commuting’, in the mathematical sense of the word commuting. Is the result of making a model and then carrying out the model process (down then right) the same as the result of the process then modelded (right then down)? In the language of the commuting diagram the question is, t ♠ ✇ ❜ Does S✦ R✦RB give the same result as S✦SB✦RB? For example, we compare the prediction of damaged plastic to what the real car damage would translate to as cracks and scratches on the plastic?