Multibody Mechanics/Notational Conventions

Throughout this text a consistent notation is maintained, which is essentially that promoted by Kane (and presented to the author with modification by Anderson). This notation eliminates the ambiguity associated with the multiple reference frames inherent in multibody analysis. It has been the author's experience in industry that too many problems are brought on by poor notation, and the notion that for some topics this notation is too rigorous has been dismissed.

Scalar quantities are represented by numbers, letters and/or symbols. The following are all scalars:

   x, $\phi$, X, $\Phi$, 3, and 5.5.

Arbitrary vectors are denoted with over-arrows as

   ${\vec {x}}$, ${\vec {\phi }}$, ${\vec {X}}$, ${\vec {\Phi }}$.

and unit vectors are given the usual hat notation

   ${\hat {i}}$, ${\hat {e}}_{\theta }$, ${\hat {a}}_{1}$.

Reference frames are labeled with a single capital letter, with 'N' being reserved for the inertial frames (also called the 'Newtonian' frame).

Each reference frame is assumed to have a set of right handed basis vectors labeled with the same lowercase letter. Basis vectors for the frame 'B' would be:

   ${\hat {b}}_{1}$, ${\hat {b}}_{2}$, ${\hat {b}}_{3}$  such that ${\hat {b}}_{1}\times {\hat {b}}_{2}={\hat {b}}_{3}$.