樹莓派、樹莓派之學習、樹莓派之教育

STEM 隨筆︰古典力學︰模擬術【二】

承上篇，那時腦海裡閃過派生『字典』

5.5. Dictionaries

Another useful data type built into Python is the dictionary (see Mapping Types — dict). Dictionaries are sometimes found in other languages as “associative memories” or “associative arrays”. Unlike sequences, which are indexed by a range of numbers, dictionaries are indexed by keys, which can be any immutable type; strings and numbers can always be keys. Tuples can be used as keys if they contain only strings, numbers, or tuples; if a tuple contains any mutable object either directly or indirectly, it cannot be used as a key. You can’t use lists as keys, since lists can be modified in place using index assignments, slice assignments, or methods like append() and extend().

It is best to think of a dictionary as an unordered set of key: value pairs, with the requirement that the keys are unique (within one dictionary). A pair of braces creates an empty dictionary: {}. Placing a comma-separated list of key:value pairs within the braces adds initial key:value pairs to the dictionary; this is also the way dictionaries are written on output.

The main operations on a dictionary are storing a value with some key and extracting the value given the key. It is also possible to delete a key:value pair with del. If you store using a key that is already in use, the old value associated with that key is forgotten. It is an error to extract a value using a non-existent key.

Performing list(d.keys()) on a dictionary returns a list of all the keys used in the dictionary, in arbitrary order (if you want it sorted, just use sorted(d.keys()) instead). [2] To check whether a single key is in the dictionary, use thein keyword.

 

資料結構本無『次序』！方才想起，只在安裝 PyDy 時，讀了一下

PyDy Package’s documentation!

 

及其範例，就匆匆上路了，果然記不牢乎？

只得自食其言，也來『補過』呦★

重讀

system

Introduction

The System class manages the simulation (integration) of a system whose equations are given by KanesMethod.

Many of the attributes are also properties, and can be directly modified.

Here is the procedure for using this class.

  1. specify your options either via the constructor or via the attributes.
  2. optionally, call generate_ode_function() if you want to customize how the ODE function is generated.
  3. call integrate() to simulate your system.

Examples

The simplest usage of this class is as follows. First, we need a KanesMethod object on which we have already invoked kanes_equations():

km = KanesMethod(...)
km.kanes_equations(force_list, body_list)
times = np.linspace(0, 5, 100)
sys = System(km, times=times)
sys.integrate()

In this case, we use defaults for the numerical values of the constants, specified quantities, initial conditions, etc. You probably won’t like these defaults. You can also specify such values via constructor keyword arguments or via the attributes:

※ 註︰ symbol 與 dynamicsymbol 須加 “s” 。此改過。

sys = System(km,
             initial_conditions={dynamicsymbols('q1'): 0.5},
             times=times)
sys.constants = {symbols('m'): 5.0}
sys.integrate()

To double-check the constants, specifieds, states and times in your problem, look at these properties:

sys.constants_symbols
sys.specifieds_symbols
sys.states
sys.times

In this case, the System generates the numerical ode function for you behind the scenes. If you want to customize how this function is generated, you must call generate_ode_function on your own:

sys = System(KM)
sys.generate_ode_function(generator='cython')
sys.integrate()

 

後，豁然開朗也☆