Description Usage Arguments Details Value Examples

Arithmetic operations for three-velocities

1 2 3 4 5 6 7 8 9 |

`e1,e2,u,v` |
Objects of class “ |

`r` |
Scalar value for circle-dot multiplication |

The function `Ops.3vel()`

passes unary and binary arithmetic
operators “`+`

”, “`-`

” and “`*`

”
to the appropriate specialist function.

The most interesting operators are “`+`

” and
“`*`

”, which are passed to `add3()`

and `dot3()`

respectively. These are defined, following Ungar, as:

*
see PDF
*

and

*
see PDF
*

where *u* and *v* are three-vectors
and *r* a scalar. Function `dot3()`

has special dispensation
for zero velocity and does not treat `NA`

entries entirely
consistently.

Arithmetic operations, executed via `Ops.4vel()`

, are not defined
on four-velocities.

The package is designed so that natural R idiom may be used for three velocity addition, see the examples section.

Returns an object of class `3vel`

, except for `prod3()`

which returns a numeric vector.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | ```
u <- as.3vel(c(-0.7, 0.1,-0.1))
v <- as.3vel(c( 0.1, 0.2, 0.3))
w <- as.3vel(c( 0.5, 0.2,-0.3))
x <- r3vel(10) # random three velocities
y <- r3vel(10) # random three velocities
u+v # add3(u,v)
u-v # add3(u,neg3(v))
-v # neg3(v)
gyr(u,v,w)
## package is vectorized:
u+x
x+y
f <- gyrfun(u,v)
g <- gyrfun(v,u)
f(g(x)) - x # should be zero by eqn10
g(f(x)) - x
(u+v) - f(v+u) # zero by eqn 10
(u+(v+w)) - ((u+v)+f(w)) # zero by eqn 11
((u+v)+w) - (u+(v+g(w))) # zero by eqn 11
## NB, R idiom is unambiguous. But always always ALWAYS use brackets.
## Ice report in lat 42.n to 41.25n Long 49w to long 50.30w saw much
## heavy pack ice and great number large icebergs also field
## ice. Weather good clear
## -u+v == (-u) + v == neg3(u) + v == add3(neg3(u),v)
## u+v+w == (u+v)+w == add3(add3(u,v),w)
``` |

RobinHankin/gyrogroup documentation built on Feb. 19, 2019, 3:20 a.m.

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