rc_animation

A module for generating animations for explaining fundamental rotation curves concepts.

ToC: Functions

CalculatePosition(radius, velocity, time, dt)

Calculates positions of multiple objects around a circle after some time with interval dt.

MultiplePositions(radius, velocity, time, dt)

Calculates transposed positions of multiple objects around a circle after some time with interval dt. Setup for the animation.

PlotRotationCurve(radius, velocity, title[, xlabel, ...])

Plot rotation curve, given the radius and velocity.

MakeAnimation(radius, velocity, time, dt, filename, title)

Animation of rotating objects around a circle.

ToC: Attributes

px

Members

rc_animation.px
rc_animation.CalculatePosition(radius, velocity, time, dt)

Calculates positions of multiple objects around a circle after some time with interval dt.

Any set of units may be used, provided they match – for example, if using a radius of meters and time in seconds, velocity should be in meters per second and the time increments should be in seconds.

Parameters:
radius[array]

Radius of the objects from the center. Units to match velocity.

velocity[array]

Velocity of the objects. Units to match radius and time. Length must match length of radius.

time[int]

Maximum time. Units to match velocity. If not divisible by dt, the final time provided may exceed this value by a number less than dt.

dt[int]

Time increment. Units to match time.

Returns:

Two [ndarray]s of x-position (first array) and y-position (second array) of all objects. These arrays are stored such that each row represents a single time and each column represents a single object. [1darray] of associated time.

Example:
>>> import numpy as np #To generate the arrays
>>> radius = np.array([1,2,3,4,5])              # in m
>>> velocity = np.array([0.1,0.2,0.3,0.4,0.5])  # in m/s
>>> time = 100                                  # in s
>>> dt = 33                                     # in s
>>> CalculatePosition(radius,velocity,time,dt)
(array([[ 1.        ,  2.        ,  3.        ,  4.        ,  5.        ],
    [-0.98747977, -1.97495954, -2.96243931, -3.94991908, -4.93739885],
    [ 0.95023259,  1.90046518,  2.85069778,  3.80093037,  4.75116296],
    [-0.88919115, -1.77838231, -2.66757346, -3.55676461, -4.44595576],
    [ 0.80588396,  1.61176792,  2.41765187,  3.22353583,  4.02941979]]),
array([[ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ],
    [-0.15774569, -0.31549139, -0.47323708, -0.63098278, -0.78872847],
    [ 0.31154136,  0.62308273,  0.93462409,  1.24616545,  1.55770682],
    [-0.45753589, -0.91507179, -1.37260768, -1.83014358, -2.28767947],
    [ 0.59207351,  1.18414703,  1.77622054,  2.36829406,  2.96036757]]),
array([  0,  33,  66,  99, 132]))
rc_animation.MultiplePositions(radius, velocity, time, dt)

Calculates transposed positions of multiple objects around a circle after some time with interval dt. Setup for the animation.

Any set of units may be used, provided they match – for example, if using a radius of meters and time in seconds, velocity should be in meters per second and the time increments should be in seconds.

Parameters:
radius[array]

Radius of the objects from the center. Units to match velocity.

velocity[array]

Velocity of the objects. Units to match radius and time. Length must match length of radius.

time[int]

Maximum time. Units to match velocity. If not divisible by dt, the final time provided may exceed this value by a number less than dt.

dt[int]

Time increment. Units to match time.

Returns:

Two [ndarray]s of x-position (first array) and y-position (second array) of all objects. These arrays are stored such that each row represents a single object and each column represents a single time. [1darray] of associated time.

Example:
>>> radius = np.array([1,2,3,4,5])              # in m
>>> velocity = np.array([0.1,0.2,0.3,0.4,0.5])  # in m/s
>>> time = 100                                  # in s
>>> dt = 50                                     # in s
>>> MultiplePositions(radius,velocity,time,dt)
(array([[ 1.        ,  0.28366219, -0.83907153],
    [ 2.        ,  0.56732437, -1.67814306],
    [ 3.        ,  0.85098656, -2.51721459],
    [ 4.        ,  1.13464874, -3.35628612],
    [ 5.        ,  1.41831093, -4.19535765]]),
array([[ 0.        , -0.95892427, -0.54402111],
    [ 0.        , -1.91784855, -1.08804222],
    [ 0.        , -2.87677282, -1.63206333],
    [ 0.        , -3.8356971 , -2.17608444],
    [ 0.        , -4.79462137, -2.72010555]]),
array([ 0, 50]))
rc_animation.PlotRotationCurve(radius, velocity, title, xlabel='Radius (km)', ylabel='Velocity (km/s)', xlim=1, ylim=0.1)

Plot rotation curve, given the radius and velocity.

Any set of units may be used, provided they match – for example, if using a radius of meters, velocity should be in meters per unit time and the labels should correctly indicate both.

Parameters:
radius[array]

Radius of the objects from the center. Units to match velocity.

velocity[array]

Velocity of the objects. Units to match radius and time. Length must match length of radius.

title[string]

Title of the plot.

xlabel[string]

X-label of the plot.

default:

‘Radius (km)’

ylabel[string]

Y-label of the plot.

default:

‘Velocity (km/s)’

xlim[float]

X-limit of the plot.

default:

1

ylim[float]

Y-limit of the plot.

default:

0.1

Returns:

None

Example:
>>> radius = np.array([1,2,3,4,5])              # in m
>>> velocity = np.array([0.1,0.2,0.3,0.4,0.5])  # in m/s
>>> PlotRotationCurve(radius,velocity,'Rigid Body Rotation Curve')
A plot, titled 'Rigid Body Rotation Curve', with the radii above on the x-axis and the velocities above on the y-axis
rc_animation.MakeAnimation(radius, velocity, time, dt, filename, title, xlim=1, ylim=1, size=False, masses=None)

Animation of rotating objects around a circle.

Any set of units may be used, provided they match – for example, if using a radius of meters and time in seconds, velocity should be in meters per second and the time increments should be in seconds.

Parameters:
radius[array]

Radius of the objects from the center. Units of km.

velocity[array]

Velocity of the objects. Units to match time with radial units of km. Length must match length of radius.

time[int]

Maximum time. Units to match velocity. If not divisible by dt, the final time provided may exceed this variable by a number less than dt.

dt[int]

Time increment. Units to match time.

filename[string]

File name to save animation.

title[string]

Title of the plot.

xlim[float]

X-limit of the plot.

default:

1

ylim[float]

Y-limit of the plot.

default:

0.1

size[bool]

Size of dots, based on masses. If True, the sizes of dots depend on masses.

default:

False

masses[array]

Masses of objects, when needed.

default:

None

Returns:

None

Example:
>>> radius = np.array([1,2,3,4,5])              # in m
>>> velocity = np.array([0.1,0.2,0.3,0.4,0.5])  # in m/s
>>> time = 100
>>> dt = 1
>>> MakeAnimation(radius, velocity, time, dt,
...     filename='images/solarsystem.gif',
...     title='Planet-like Rotation')
An animation of planet-like rotation, in which the five planets are, coincidentally, moving like a rigid body. The x-axis and y-axis are both labeled with units of km with ranges of -6 to +6. Below the title 'Planet-like Rotation' is a counter indicating the current number of seconds, in scientific notation, resetting itself periodically. Other than this timer, the animation appears continuious.