Related Essential Functions (Docstrings)

dynamicsymbols

sympy.physics.mechanics.essential.dynamicsymbols(names, level=0)

Uses symbols and Function for functions of time.

Creates a SymPy UndefinedFunction, which is then initialized as a function of a variable, the default being Symbol(‘t’).

Parameters :

names : str

Names of the dynamic symbols you want to create; works the same way as inputs to symbols

level : int

Level of differentiation of the returned function; d/dt once of t, twice of t, etc.

Examples :

======= :

>>> from sympy.physics.mechanics import dynamicsymbols :

>>> from sympy import diff, Symbol :

>>> q1 = dynamicsymbols(‘q1’) :

>>> q1 :

q1(t) :

>>> diff(q1, Symbol(‘t’)) :

Derivative(q1(t), t) :

dot

sympy.physics.mechanics.functions.dot(vec1, vec2)

Dot product convenience wrapper for Vector.dot(): Dot product of two vectors.

Returns a scalar, the dot product of the two Vectors

Parameters :

other : Vector

The Vector which we are dotting with

Examples

>>> from sympy.physics.mechanics import ReferenceFrame, Vector, dot
>>> from sympy import symbols
>>> q1 = symbols('q1')
>>> N = ReferenceFrame('N')
>>> dot(N.x, N.x)
1
>>> dot(N.x, N.y)
0
>>> A = N.orientnew('A', 'Axis', [q1, N.x])
>>> dot(N.y, A.y)
cos(q1)

cross

sympy.physics.mechanics.functions.cross(vec1, vec2)

Cross product convenience wrapper for Vector.cross(): The cross product operator for two Vectors.

Returns a Vector, expressed in the same ReferenceFrames as self.

Parameters :

other : Vector

The Vector which we are crossing with

Examples

>>> from sympy.physics.mechanics import ReferenceFrame, Vector
>>> from sympy import symbols
>>> q1 = symbols('q1')
>>> N = ReferenceFrame('N')
>>> N.x ^ N.y
N.z
>>> A = N.orientnew('A', 'Axis', [q1, N.x])
>>> A.x ^ N.y
N.z
>>> N.y ^ A.x
- sin(q1)*A.y - cos(q1)*A.z

outer

sympy.physics.mechanics.functions.outer(vec1, vec2)

Outer prodcut convenience wrapper for Vector.outer(): Returns a vector, expressed in the other frame.

A new Vector is returned, equalivalent to this Vector, but its components are all defined in only the otherframe.

Parameters :

otherframe : ReferenceFrame

The frame for this Vector to be described in

Examples

>>> from sympy.physics.mechanics import ReferenceFrame, Vector, dynamicsymbols
>>> q1 = dynamicsymbols('q1')
>>> N = ReferenceFrame('N')
>>> A = N.orientnew('A', 'Axis', [q1, N.y])
>>> A.x.express(N)
cos(q1)*N.x - sin(q1)*N.z

express

sympy.physics.mechanics.functions.express(vec, frame, frame2=None)

Express convenience wrapper for Vector.express(): Returns a vector, expressed in the other frame.

A new Vector is returned, equalivalent to this Vector, but its components are all defined in only the otherframe.

Parameters :

otherframe : ReferenceFrame

The frame for this Vector to be described in

Examples

>>> from sympy.physics.mechanics import ReferenceFrame, Vector, dynamicsymbols
>>> q1 = dynamicsymbols('q1')
>>> N = ReferenceFrame('N')
>>> A = N.orientnew('A', 'Axis', [q1, N.y])
>>> A.x.express(N)
cos(q1)*N.x - sin(q1)*N.z