Difference between revisions of "Forest UCM NLM"
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==Vector Notation== | ==Vector Notation== | ||
| − | A vector is a mathematical construct | + | A vector is a mathematical construct of ordered elements that represent magnitude and direction simultaneously. |
:<math>\vec{r} = x \hat{i} + y \hat{j} + z \hat{k} = (x,y,z) = \sum_1^3 r_i \hat{e}_i</math> | :<math>\vec{r} = x \hat{i} + y \hat{j} + z \hat{k} = (x,y,z) = \sum_1^3 r_i \hat{e}_i</math> | ||
| Line 25: | Line 25: | ||
The multiplication of two vectors is not uniquely defined. At least three types of vector products may be defined. | The multiplication of two vectors is not uniquely defined. At least three types of vector products may be defined. | ||
| + | |||
== Scaler ( Dot ) product== | == Scaler ( Dot ) product== | ||
Revision as of 21:54, 15 July 2014
Newton's Laws of Motion
Limits of Classical Mechanic
Classical Mechanics is the formulations of physics developed by Newton (1642-1727), Lagrange(1736-1813), and Hamilton(1805-1865).
It may be used to describe the motion of objects which are not moving at high speeds (0.1) nor are microscopically small ( ).
The laws are formulated in terms of space, time, mass, and force:
Vectors
Vector Notation
A vector is a mathematical construct of ordered elements that represent magnitude and direction simultaneously.
Vectors satisfy the commutative (order of addition doesn't matter) and associative ( doesn't matter which you add first) properties.
The multiplication of two vectors is not uniquely defined. At least three types of vector products may be defined.
Scaler ( Dot ) product
Vector ( Cross ) product
A third vector product is the tensor direct product.
Space and Time
Space
Cartesian, Spherical, and Cylindrical coordinate systems are commonly used to describe three-dimensional space.