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# # Geometry of motion - kinematics
#
# # Position
#
# Classical physics describes the position of an object using three
# independent coordinates e.g. 
#
# $\mathbf{r}_{P/O} = x\hat{i} + y\hat{j} + z\hat{k}$
#
# where $\mathbf{r}_{P/O}$ is the position of point $P$ _with respect to the point
# of origin_ $O$, $x,~y,~z$ are magnitudes of distance along a
# Cartesian coordinate system and $\hat{i},~\hat{j}$ and $\hat{k}$ are
# unit vectors that describe three 

import numpy as np
r = np.array([1,2,3])
print(r)

# # Velocity
#
# The velocity of an object is the change in position per length of time.
#
# $\mathbf{v}_{P/O} = \frac{d\mathbf{r}_{P/O}}{dt} = \dot{x}\hat{i} + \dot{y}\hat{j} +
# \dot{z}\hat{k}$
#
# This definition of velocity depends upon the change in position of all
# three independent coordinates, where
# $\frac{d}{dt}(x\hat{i})=\dot{x}\hat{i}$. 
#
# ## Speed
#
# The speed of an object is the
# [magnitude](https://www.mathsisfun.com/algebra/vectors.html) of the
# velocity, 
#
# $|\mathbf{v}_{P/O}| = \sqrt{\mathbf{v}\cdot\mathbf{v}} =
# \sqrt{\dot{x}^2 + \dot{y}^2 + \dot{z}^2}$
#
# # Acceleration
#
# The acceleration of an object is the change in velocity per length of
# time. 
#
# $\mathbf{a}_{P/O} = \frac{d \mathbf{v}_{P/O} }{dt} = \ddot{x}\hat{i} +
# \ddot{y}\hat{j} + \ddot{z}\hat{k}$
#
# where $\ddot{x}=\frac{d^2 x}{dt^2}$ and $\mathbf{a}_{P/O}$ is the
# acceleration of point $P$ _with respect to the point of origin_ $O$. 
#
# # Rotation _in planar motion_
#
# The definitions of position, velocity, and acceleration all describe a
# single point, but dynamic engineering systems are composed of rigid
# bodies is needed to describe the position of an object. 

from IPython.core.display import SVG
SVG(filename='../dyn-logo.svg')

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