By Jazar R.N.
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Extra info for Advanced Dynamics
The path of the motion of a particle is a curve in space. The analytic equation of the space curve is used to determine the vectorial expression of kinematics of the moving point. 13. The curve Gr = Gr (q) reduces to a point on C if we ﬁx the parameter q. 224) are the parametric equations of the curve. 225) The arc length of a curve is deﬁned as the limit of the diagonal of a rectangular box as the length of the sides uniformly approach zero. 227) where α, β, and γ are the directional cosines of the line.
5 O O O O y y y y (c) (d) (a) A vecpoint, (b) a vecline, (c) a vecface, and (d ) a vecfree. 6 (a) a vecpoline, (b) vecpoface, (c) vecporee. 7. Vecporee. When the start point of a vector is ﬁxed and the end point can move anywhere in a speciﬁed space, the vector is called a point-free vector or vecporee. Such a vector has a variable length and orientation. 6 illustrates a vecpoline, a vecpoface, and a vecporee. We may compare two vectors only if they represent the same physical quantity and are expressed in the same coordinate frame.
Example 10 Scalars Physical quantities which can be speciﬁed by only a number are called scalars. If a physical quantity can be represented by a scalar, it is called a scalaric physical quantity. We may compare two scalars only if they represent the same physical quantity. Temperature, density, and work are some examples of scalaric physical quantities. Two scalars are equal if they represent the same scalaric physical quantity and they have the same number in the same system of units. Two scalars are equivalent if we can substitute one with the other.
Advanced Dynamics by Jazar R.N.