Difference between revisions of "Forest UCM NLM"

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Vector Notation convention:
 
Vector Notation convention:
  
Position:<math>\vec{r} = x \hat{i} + y \hat{j} + z \hat{k} = (x,y,z) = \sum_1^3 r_i \hat{e}_i</math>
+
Position:
 +
 
 +
;<math>\vec{r} = x \hat{i} + y \hat{j} + z \hat{k} = (x,y,z) = \sum_1^3 r_i \hat{e}_i</math>
  
 
Velocity:  
 
Velocity:  
<math>\vec{v}</math> = <math>\frac{d \vec{r}}{dt}</math> = <math>\frac{d x}{dt}\hat{i} + x\frac{d \hat{i}}{dt} + …</math> =
+
 
 +
:<math>\vec{v}</math> = <math>\frac{d \vec{r}}{dt}</math> = <math>\frac{d x}{dt}\hat{i} + x\frac{d \hat{i}}{dt} + …</math> =
  
 
===Spherical===
 
===Spherical===

Revision as of 18:27, 12 June 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[math] c[/math]) nor are microscopically small ( [math]10^{-9} m[/math]).

The laws are formulated in terms of space, time, mass, and force:

Space and Time

Space

Cartesian, Spherical, and Cylindrical coordinate systems are commonly used to describe three-dimensional space.

Cartesian

TF UCM CartCoordSys.png


Vector Notation convention:

Position:

[math]\vec{r} = x \hat{i} + y \hat{j} + z \hat{k} = (x,y,z) = \sum_1^3 r_i \hat{e}_i[/math]

Velocity:

[math]\vec{v}[/math] = [math]\frac{d \vec{r}}{dt}[/math] = [math]\frac{d x}{dt}\hat{i} + x\frac{d \hat{i}}{dt} + …[/math] =

Spherical

TF UCM SphericalCoordSys.png

Cylindrical

TF UCM CylCoordSys.png

Vectors

Scaler ( Dot ) product

Vector ( Cross ) product

Forest_Ugrad_ClassicalMechanics