aarjaneiro/planetmath huggingface dataset:
tacit extension

tacit extension

A

tacit extension

is an

injection

of a set into a

Cartesian product

that has that set as one of its factors. There are many such injections, all of which serve as

inverse

operations

to the projection of the Cartesian product onto the set in question, but the tacit extension is the one that places no additional constraints on the injection

mapping

.

Title

tacit extension

Canonical

name

TacitExtension

Date of creation

2013-03-22 17:49:45

Last modified on

2013-03-22 17:49:45

Owner

Jon Awbrey (15246)

Last modified by

Jon Awbrey (15246)

Numerical id

5

Author

Jon Awbrey (15246)

Entry type

Definition

Classification

msc 68R01

Classification

msc 68P15

Classification

msc 08A02

Classification

msc 05C65

Classification

msc 05B30

Classification

msc 05B20

Classification

msc 03E20

Classification

msc 03B10

Synonym

inverse projection

Related topic

Projection

Related topic

RelationComposition2

Related topic

RelationReduction

Related topic

RelationConstruction

Generated on Sat Feb 10 12:50:17 2018 by

LaTeXML
digital library structure

digital library structure

A

digital library structure

is a triplet

(

G

,

L

,

F

)

, where

G

=

(

V

,

E

)

is a

directed graph

with a

vertex set

V

and

edge set

E

,

L

is a set of label values, and

F

is

labeling

function

F

:

(

V

∪

E

)

→

L

.

Title

digital library structure

Canonical name

DigitalLibraryStructure

Date of creation

2013-03-22 14:05:22

Last modified on

2013-03-22 14:05:22

Owner

mathcam (2727)

Last modified by

mathcam (2727)

Numerical id

5

Author

mathcam (2727)

Entry type

Definition

Classification

msc 68R10

Generated on Sat Feb 10 12:50:19 2018 by

LaTeXML
Floyd’s algorithm

Floyd’s algorithm

Floyd’s

algorithm

is also known as the all pairs

shortest path algorithm

. It will compute the shortest path between all possible pairs of vertices in a (possibly weighted) graph or

digraph

simultaneously in

O

⁢

(

n

3

)

time (where

n

is the number of vertices in the graph).

Algorithm

Floyd

(V)

Input

: A

weighted graph

or digraph with vertices

V

Output

: A matrix

c

⁢

o

⁢

s

⁢

t

of shortest paths and a matrix

p

⁢

r

⁢

e

⁢

d

of predecessors in the shortest path

for

(

a

,

b

)

∈

V

2

do

if

a

⁢

d

⁢

j

⁢

a

⁢

c

⁢

e

⁢

n

⁢

t

⁢

(

a

,

b

)

then

c

⁢

o

⁢

s

⁢

t

⁢

(

a

,

b

)

←

w

⁢

e

⁢

i

⁢

g

⁢

h

⁢

t

⁢

(

a

,

b

)

p

⁢

r

⁢

e

⁢

d

⁢

(

a

,

b

)

←

a

else

c

⁢

o

⁢

s

⁢

t

⁢

(

a

,

b

)

←

∞

p

⁢

r

⁢

e

⁢

d

⁢

(

a

,

b

)

←

n

⁢

u

⁢

l

⁢

l

for

c

∈

V

do

for

(

a

,

b

)

∈

V

2

do

if

c

⁢

o

⁢

s

⁢

t

⁢

(

a

,

c

)

<

∞

and

c

⁢

o

⁢

s

⁢

t

⁢

(

c

,

b

)

<

∞

then

if

c

⁢

o

⁢

s

⁢

t

⁢

(

a

,

b

)

=

∞

or

c

⁢

o

⁢

s

⁢

t

⁢

(

a

,

c

)

+

c

⁢

o

⁢

s

⁢

t

⁢

(

c

,

b

)

<

c

⁢

o

⁢

s

⁢

t

⁢

(

a

,

b

)

then

c

⁢

o

⁢

s

⁢

t

⁢

(

a

,

b

)

←

c

⁢

o

⁢

s

⁢

t

⁢

(

a

,

c

)

+

c

⁢

o

⁢

s

⁢

t

⁢

(

c

,

b

)

p

⁢

r

⁢

e

⁢

d

⁢

(

a

,

b

)

←

p

⁢

r

⁢

e

⁢

d

⁢

(

c

,

b

)

Title

Floyd’s algorithm

Canonical name

FloydsAlgorithm

Date of creation

2013-03-22 12:16:29

Last modified on

2013-03-22 12:16:29

Owner

vampyr (22)

Last modified by

vampyr (22)

Numerical id

6

Author

vampyr (22)

Entry type

Algorithm

Classification

msc 68R10

Classification

msc 05C38

Classification

msc 05C85

Synonym

all pairs shortest path algorithm

Generated on Sat Feb 10 12:50:21 2018 by

LaTeXML
aliasing

aliasing

Aliasing

Used in the context of processing digitized signals (e.g. audio) and images (e.g. video), aliasing describes the effect of undersampling during digitization which can generate a false (apparent) low frequency for signals, or staircase steps along edges in images (jaggies.) Aliasing can be avoided by an antialiasing (analogue) low-pass filter, before sampling. The term antialiasing is also in use for

a posteriori

signal smoothing intended to remove the effect.

References

•

Based on content from The Data Analysis Briefbook (

http://rkb.home.cern.ch/rkb/titleA.html

http://rkb.home.cern.ch/rkb/titleA.html)

Title

aliasing

Canonical

name

Aliasing

Date of creation

2013-03-22 12:04:23

Last modified on

2013-03-22 12:04:23

Owner

akrowne (2)

Last modified by

akrowne (2)

Numerical id

8

Author

akrowne (2)

Entry type

Definition

Classification

msc 68U10

Classification

msc 94A08

Generated on Sat Feb 10 12:50:28 2018 by

LaTeXML
precision recall

precision recall

In information retrieval, precision and recall are the fundamental

parameters

defining the behavior of an information retrieval system. Precision is defined as the proportion of relevant documents in the set of all documents returned by a search. Recall is defined as the number of relevant documents retrieved as fraction of all relevant documents.

Title

precision recall

Canonical

name

PrecisionRecall

Date of creation

2013-03-22 15:31:46

Last modified on

2013-03-22 15:31:46

Owner

bzhang (11006)

Last modified by

bzhang (11006)

Numerical id

7

Author

bzhang (11006)

Entry type

Definition

Classification

msc 68U35

Generated on Sat Feb 10 12:50:29 2018 by

LaTeXML
Horner’s rule

Horner’s rule

Horner’s rule is a technique to reduce the work required for the

computation

of a

polynomial

at a particular value. Its simplest form makes use of the repeated

factorizations

y

=

a

0

+

a

1

⁢

x

+

a

2

⁢

x

2

+

⋯

+

a

n

⁢

x

n

=

a

0

+

x

⁢

(

a

1

+

x

⁢

(

a

2

+

x

⁢

(

a

3

+

⋯

+

x

⁢

a

n

)

)

⁢

⋯

)

of the terms of the

n

th degree polynomial in

x

in order to reduce the computation of the polynomial

y

⁢

(

a

)

(at some value

x

=

a

) to

n

multiplications

and

n

additions

.

The rule can be generalized to a finite series

y

=

a

0

⁢

p

0

+

a

1

⁢

p

1

+

⋯

+

a

n

⁢

p

n

of

orthogonal polynomials

p

k

=

p

k

⁢

(

x

)

. Using the

recurrence relation

p

k

=

(

A

k

+

B

k

⁢

x

)

⁢

p

k

-

1

+

C

k

⁢

p

k

-

2

for orthogonal polynomials, one obtains

y

⁢

(

a

)

=

(

a

0

+

C

2

⁢

b

2

)

⁢

p

0

⁢

(

a

)

+

b

1

⁢

p

1

⁢

(

a

)

with

b

n

+

1

=

b

n

+

2

=

0

,

b

k

-

1

=

(

A

k

+

B

k

⋅

a

)

⁢

b

k

+

C

k

+

1

+

b

k

+

1

+

a

k

-

1

for the evaluation of

y

at some particular

a

. This is a simpler calculation than the straightforward approach, since

a

0

and

C

2

are known,

p

0

⁢

(

a

)

and

p

1

⁢

(

a

)

are easy to compute (possibly themselves by Horner’s rule), and

b

1

and

b

2

are given by a backwards-recurrence which is linear in

n

.

References

•

Originally from The Data Analysis Briefbook
(

http://rkb.home.cern.ch/rkb/titleA.html

http://rkb.home.cern.ch/rkb/titleA.html)

Title

Horner’s rule

Canonical name

HornersRule

Date of creation

2013-03-22 12:06:17

Last modified on

2013-03-22 12:06:17

Owner

akrowne (2)

Last modified by

akrowne (2)

Numerical id

11

Author

akrowne (2)

Entry type

Algorithm

Classification

msc 68W01

Classification

msc 13P05

Classification

msc 65Y99

Generated on Sat Feb 10 12:50:34 2018 by

LaTeXML
FORTRAN

FORTRAN

FORTRAN

1

1

Acronym that comes from

For-mula Tran-slating.

(or

ForTran

or

Fortran

) is a

computer

programming language developed by IBM in the 1950s with a focus on scientific and engineering applications. FORTRAN is still in use today in the sciences despite the

dominance

of C++ (

http://planetmath.org/C

) for most general applications and

Mathematica

and Maple for

algebra

applications. Sloane’s

On-Line Encyclopedia of Integer Sequences

does not include FORTRAN source code but provides links to it. The current version is FORTRAN 2003; an international group of corporations and programmers is working on FORTRAN 2008.

The following FORTRAN

program

takes two

integers

as inputs and outputs their

greatest common divisor

using Euclid’s

algorithm

. It requires

positive integers

as inputs. NB is just a

variable

name that has nothing to do with Zentrums. The

function

NGCD is defined after the main program. It was written by Wikipedia user Rwwww:

* euclid.f (FORTRAN 77)
* Find greatest common divisor using the Euclidean algorithm
* Written by: Wikipedia User:Rwwww

PROGRAM EUCLID
PRINT *, 'A?'
READ *, NA
IF (NA.LE.0) THEN
PRINT *, 'A must be a positive integer.'
STOP
END IF
PRINT *, 'B?'
READ *, NB
IF (NB.LE.0) THEN
PRINT *, 'B must be a positive integer.'
STOP
END IF
PRINT *, 'The GCD of', NA, ' and', NB, ' is', NGCD(NA, NB), '.'
STOP
END

FUNCTION NGCD(NA, NB)
IA = NA
IB = NB
1 IF (IB.NE.0) THEN
ITEMP = IA
IA = IB
IB = MOD(ITEMP, IB)
GOTO 1
END IF
NGCD = IA
RETURN
END

Title

FORTRAN

Canonical

name

FORTRAN

Date of creation

2013-03-22 16:46:38

Last modified on

2013-03-22 16:46:38

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

9

Author

PrimeFan (13766)

Entry type

Topic

Classification

msc 68W30

Classification

msc 68N15

Generated on Sat Feb 10 12:50:39 2018 by

LaTeXML
list of name and Greek letter functions and constants in Mathematica

list of name and Greek letter functions and constants in Mathematica

In

Mathematica

, certain important mathematical

functions

or constants are built-in and given the name of the mathematician who came up with the function followed by the romanization of the Greek letter most commonly used for the function.

EulerGamma

The Euler-Mascheroni constant

γ

StieltjesGamma[n]

Stieltjes constant

γ

⁢

n

CarmichaelLambda[n]

Carmichael function

λ

⁢

(

n

)

MoebiusMu[n]

Möbius function

μ

⁢

(

n

)

LerchPhi[z, s, a]

Lerch function

Φ

⁢

(

z

,

s

,

a

)

EulerPhi[n]

Euler totient function

ϕ

⁢

(

n

)

RamanujanTau[n]

Ramanujan function

τ

⁢

(

n

)

RamanujanTauL[x]

Ramanujan

τ

Dirichlet L function

L

⁢

(

x

)

Note that the

Riemann zeta function

ζ

⁢

(

x

)

is invoked by

Zeta[x]

and not

RiemannZeta[x]

.

Title

list of name and Greek letter functions and constants in Mathematica

Canonical name

ListOfNameAndGreekLetterFunctionsAndConstantsInMathematica

Date of creation

2013-03-22 17:13:55

Last modified on

2013-03-22 17:13:55

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

4

Author

PrimeFan (13766)

Entry type

Data Structure

Classification

msc 68W30

Generated on Sat Feb 10 12:50:40 2018 by

LaTeXML
MATLAB

MATLAB

MATLAB

, short for

MATrix LABoratory

, is a

computer algebra system

produced by MathWorks. It was developed by Cleve Moler at the University of New Mexico, the first commercial version came out in 1984. The syntax of MATLAB is called

M-code

. Optionally, MATLAB can be coupled with the Maple kernel.

http://www.mathworks.com/products/matlab/

Official website

Title

MATLAB

Canonical name

MATLAB

Date of creation

2013-03-22 16:21:57

Last modified on

2013-03-22 16:21:57

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

4

Author

Mravinci (12996)

Entry type

Definition

Classification

msc 68W30

Synonym

MATrix LABoratory

Defines

M-code

Generated on Sat Feb 10 12:50:42 2018 by

LaTeXML
Maple

Maple

Maple

is a

computer algebra system

produced by Maplesoft. The first version, developed by the University of Waterloo in Ontario, Canada, came out in 1981. The most recent version is 11.0. The

program

is named for a popular Canadian tree.

Like

Mathematica

, Maple has its own field in the

On-Line Encyclopedia of Integer Sequences

.

http://www.maplesoft.com/

Official website

Title

Maple

Canonical

name

Maple

Date of creation

2013-03-22 16:21:49

Last modified on

2013-03-22 16:21:49

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

6

Author

Mravinci (12996)

Entry type

Topic

Classification

msc 68W30

Generated on Sat Feb 10 12:50:43 2018 by

LaTeXML
Mathematica

Mathematica

Mathematica

is a

computer algebra system

produced by Wolfram Research. The first publically available version, 1.0, came out in 1988, the most recent, 5.2, in 2005. Although primarily intended for

algebraic

and

arithmetic

computations

, Mathematica is also capable of text manipulation and graphics.

The standard installation provides a kernel that does the work of performing the computations requested by the user and a front-end that displays the input and output; the two communicate using ”MathLink.” Wolfram provides an API for using a different kernel or front-end.

The standard front-end can execute commands whether they are written as they would in a programming language (e.g., “

Sqrt[Pi^e]

”) or typeset using the palettes (e.g., “

π

e

”).

Error messages are usually given in blue text but do not require clearance by a special key (as they would in a stand-alone

calculator

).

Division by zero

gives the error message “Power::infy: Infinite expression

1

0

encountered” and the result “ComplexInfinity”.

0

0

gives the error message “Power::indet::

Indeterminate

expression

0

0

encountered” and the result “Indeterminate”. In some

contexts

Mathematica will attempt to guess what kind of result the user wants for these

infinite

or indeterminate expressions, such as when taking certain limits.

Unix and Linux installations include a command-line front-end that can only accept commands in the former)

Like Maple, Mathematica has its own field in the

On-Line Encyclopedia of Integer Sequences

.
A detailed, critical review of Mathematica is given

http://www.cs.berkeley.edu/ fateman/papers/mma.review.pdf

here.

http://www.wolfram.com/products/mathematica/index.html

Official website

References

1

Kevin R. Coombes, Brian R. Hunt, Ronald L. Lipsman, John E. Osborn & Garrett J. Stuck,

The Mathematica Primer

. Cambridge: Cambridge University Press (1998)

2

Jerry Glynn & Theodore Gray,

The Beginner’s Guide to Mathematica Version 4

. Cambridge: Cambridge University Press (2000)

3

Bruce F. Torrence & Eve A. Torrence,

The Student’s Introduction to Mathematica: A Handbook for Precalculus, Calculus, and

Linear Algebra

. Cambridge: Cambridge University Press (1999)

4

S. Wolfram,

The Mathematica Book

, 4th Ed. Cambridge: Cambridge University Press (1999): 3.1.8

Title

Mathematica

Canonical

name

Mathematica

Date of creation

2013-03-22 16:21:46

Last modified on

2013-03-22 16:21:46

Owner

Mravinci (12996)

Last modified by

Mravinci (12996)

Numerical id

11

Author

Mravinci (12996)

Entry type

Topic

Classification

msc 68W30

Generated on Sat Feb 10 12:50:45 2018 by

LaTeXML
speedup

speedup

Speedup

is a way to quantify the advantage of using a parallel algorithm over a sequential algorithm. The speedup

S

is defined as

S

=

R

P

Where

R

is the running time of the best available sequential algorithm and

P

is the running time of the parallel algorithm.

Ideally, on a system with

N

processors, the speedup for any

algorithm

would be

N

. Amdahl’s law deals with the speedup in more realistic situations.

Title

speedup

Canonical name

Speedup

Date of creation

2013-03-22 12:04:12

Last modified on

2013-03-22 12:04:12

Owner

akrowne (2)

Last modified by

akrowne (2)

Numerical id

6

Author

akrowne (2)

Entry type

Definition

Classification

msc 68W40

Classification

msc 68W10

Generated on Sat Feb 10 12:50:46 2018 by

LaTeXML
particle moving on a cardioid at constant frequency

particle moving on a cardioid at constant frequency

This is another elementary example

1

1

C.F. particle moving on the

astroid

at constant frequency

about particle kinematics. In this case we will use

polar coordinates

. Let us consider the

cardioid

2

2

the locus of the points of the plane described by a circle (or disc) boundary point which it is rolling over another one with the same radius

R

.

r

=

4

⁢

R

⁢

cos

2

⁡

ω

⁢

t

2

,

3

3

indeed the native

polar equation

of the cardioid is

r

=

2

⁢

R

⁢

(

1

+

cos

⁡

θ

)

,

θ

=

ω

⁢

t

.

with

R

,

ω

>

0

given constants and

t

∈

[

0

,

∞

)

means time parameter. The position vector of a particle, respect to an orthonormal reference basis

{

𝐫

^

,

θ

^

}

,

moving on the cardioid is

𝐫

=

4

⁢

R

⁢

cos

2

⁡

ω

⁢

t

2

⁢

𝐫

^

,

and its

velocity

4

4

in polar coordinates we have

𝐫

˙

=

r

˙

⁢

𝐫

^

+

r

⁢

θ

˙

⁢

θ

^

,

because the base vectors

𝐫

^

,

θ

^

are changing on direction and sense according the formulas

d

⁢

𝐫

^

d

⁢

θ

=

θ

^

,

d

⁢

θ

^

d

⁢

θ

=

-

𝐫

^

.

We are using the

chain rule

with

θ

˙

=

ω

.

Overdot denotes time

differentiation

everywhere.

𝐯

=

𝐫

˙

=

-

4

⁢

R

⁢

ω

⁢

sin

⁡

ω

⁢

t

2

⁢

cos

⁡

ω

⁢

t

2

⁢

𝐫

^

+

4

⁢

R

⁢

ω

⁢

cos

2

⁡

ω

⁢

t

2

⁢

θ

^

.

Therefore the speed is

v

=

4

⁢

R

⁢

ω

⁢

cos

⁡

ω

⁢

t

2

,

and the

tangent vector

𝐓

=

-

sin

⁡

ω

⁢

t

2

⁢

𝐫

^

+

cos

⁡

ω

⁢

t

2

⁢

θ

^

.

Next we use the formula

v

ρ

:=

∥

𝐓

˙

∥

=

∥

-

ω

2

⁢

cos

⁡

ω

⁢

t

2

⁢

𝐫

^

-

sin

⁡

ω

⁢

t

2

⁢

𝐫

^

˙

-

ω

2

⁢

sin

⁡

ω

⁢

t

2

⁢

θ

^

+

cos

⁡

ω

⁢

t

2

⁢

θ

^

˙

∥

,

and by using the time derivative of base vectors

v

ρ

=

∥

-

3

⁢

ω

2

⁢

cos

⁡

ω

⁢

t

2

⁢

𝐫

^

-

3

⁢

ω

2

⁢

sin

⁡

ω

⁢

t

2

⁢

θ

^

∥

,

getting the equation

v

=

3

2

⁢

ω

⁢

ρ

.

Title

particle moving on a cardioid at constant frequency

Canonical name

ParticleMovingOnACardioidAtConstantFrequency

Date of creation

2013-03-22 17:14:20

Last modified on

2013-03-22 17:14:20

Owner

perucho (2192)

Last modified by

perucho (2192)

Numerical id

6

Author

perucho (2192)

Entry type

Topic

Classification

msc 70B05

Generated on Sat Feb 10 12:51:08 2018 by

LaTeXML
particle moving on the astroid at constant frequency

particle moving on the astroid at constant frequency

In parametric Cartesian equations, the astroid can be represented by

x

=

a

⁢

cos

3

⁡

ω

⁢

t

,

y

=

a

⁢

sin

3

⁡

ω

⁢

t

,

where

a

>

0

is a known constant,

ω

>

0

is the constant angular frequency, and

t

∈

[

0

,

∞

)

is the time parameter. Thus the

position vector

of a particle, moving over the astroid, is

𝐫

=

a

⁢

cos

3

⁡

ω

⁢

t

⁢

𝐢

+

a

⁢

sin

3

⁡

ω

⁢

t

⁢

𝐣

,

and its

velocity

𝐯

=

-

3

⁢

a

⁢

ω

⁢

sin

⁡

ω

⁢

t

⁢

cos

2

⁡

ω

⁢

t

⁢

𝐢

+

3

⁢

a

⁢

ω

⁢

sin

2

⁡

ω

⁢

t

⁢

cos

⁡

ω

⁢

t

⁢

𝐣

,

where

{

𝐢

,

𝐣

}

is a reference basis. Hence for the particle speed we have

v

=

3

⁢

a

⁢

ω

⁢

sin

⁡

ω

⁢

t

⁢

cos

⁡

ω

⁢

t

.

From the last two equations we get the

tangent vector

𝐓

=

-

sin

⁡

ω

⁢

t

⁢

𝐢

+

cos

⁡

ω

⁢

t

⁢

𝐣

,

and by using the well known formula

1

1

By applying the

chain rule

,

∥

d

⁢

𝐓

d

⁢

t

∥

=

∥

d

⁢

𝐓

d

⁢

s

∥

⁢

|

d

⁢

s

d

⁢

t

|

=

∥

𝐍

ρ

∥

⁢

v

=

v

ρ

,

by Frenet-Serret.

𝐍

is the

normal vector

.

∥

d

⁢

𝐓

d

⁢

t

∥

=

v

ρ

,

ρ

>

0

being the

radius of curvature

at any instant

t

, we arrive to the useful equation

v

=

ω

⁢

ρ

.

Title

particle moving on the astroid at constant frequency

Canonical name

ParticleMovingOnTheAstroidAtConstantFrequency

Date of creation

2013-03-22 17:14:09

Last modified on

2013-03-22 17:14:09

Owner

perucho (2192)

Last modified by

perucho (2192)

Numerical id

9

Author

perucho (2192)

Entry type

Topic

Classification

msc 70B05

Generated on Sat Feb 10 12:51:10 2018 by

LaTeXML
Euler’s equation for rigid bodies

Euler’s equation for rigid bodies

Let

1

be an inertial frame body (a rigid body) and

2

a rigid body in motion respect to an observer located at

1

. Let

Q

be an arbitrary point (fixed or in motion) and

C

the center of mass of

2

. Then,

𝐌

Q

=

I

Q

⁢

𝜶

21

+

𝝎

21

×

(

I

Q

⁢

𝝎

21

)

+

m

⁢

𝐐𝐂

¯

×

𝐚

1

Q

⁢

2

,

(1)

where

m

is the mass of the rigid body,

𝐐𝐂

¯

the

position vector

of

C

respect to

Q

,

𝐌

Q

is the moment of forces system respect to

Q

,

I

Q

the tensor of inertia respect to

orthogonal

axes embedded in

2

and origin at

Q

⁢

2

1

1

That is possible because the kinematical

concept

of frame

extension

.

, and

𝐚

1

Q

⁢

2

,

𝝎

21

,

𝜶

21

, are the acceleration of

Q

⁢

2

, the angular velocity and acceleration vectors respectively, all of them measured by an observer located at

1

.

This

equation

was got by Euler by using a fixed system of principal axes with origin at

C

⁢

2

. In that case we have

Q

=

C

, and therefore

𝐌

C

=

I

C

⁢

𝜶

21

+

𝝎

21

×

(

I

C

⁢

𝝎

21

)

.

(2)

Euler used three

independent

scalar equations to represent (2). It is well known that the number of degrees of freedom associate to a rigid body in free motion in

ℝ

3

are six, just equal the number of independent scalar equations necessary to solve such a motion. (Newton’s law contributing with three)

Its is clear if

2

is at rest or in uniform and rectilinear

translation

, then

𝐌

Q

=

𝟎

, one of the necessary and sufficient conditions for the equilibrium of the system of forces applied to a rigid body. (The other one is the force resultant

𝐅

=

𝟎

)

Title

Euler’s equation for rigid bodies

Canonical name

EulersEquationForRigidBodies

Date of creation

2013-03-22 17:10:36

Last modified on

2013-03-22 17:10:36

Owner

perucho (2192)

Last modified by

perucho (2192)

Numerical id

8

Author

perucho (2192)

Entry type

Topic

Classification

msc 70G45

Generated on Sat Feb 10 12:51:16 2018 by

LaTeXML