Sage 3d Vector Field

Vector fields provide an interesting way to look at the world.

Sage 3d vector field. Var y1 y2 vfield vector y1 y2 y1 y2 plot vector field vfield y1 5 5 y2 5 5 sometimes it is convenient to plot the normalized version of the vector field. Below are the sage commands for plotting 2d and 3d vector fields. Functions a list of three functions representing the x y and z coordinates of a vector. The vector representing this motion has magnitude 100 km h and direction north.

For instance the. First a quick bit of background. As always start by declaring that x y and z are variables. Plotting 3d fields sage plot plot3d plot field3d plot vector field3d functions xrange yrange zrange plot points 5 colors jet center arrows false kwds plot a 3d vector field.

Change the components of the vector field by typing for example. This is the only memory efficient implementation. If vec f is a conservative vector field then the function f is called a potential function for vec f. In other words various charts and frames can be introduced on the manifold and a given tensor field can have representations in each of them.

Note that jmol is still available via the option viewer jmol in the plot functions. Hit ctrl enter to execute a line of code x y z var x y z. Sage plot plot field plot slope field f xrange yrange kwds plot slope field takes a function of two variables xvar and yvar for instance if the variables are x and y take f x y and at representative points xi yi between xmin xmax and ymin ymax respectively plots a line with slope f xi yi see below. Change the scale to provide a better visualisation of the vector field.

A vector field vec f is called a conservative vector field if there exists a function f such that vec f nabla f. Sage uses a new algorithm to obtain the f vector for polyhedra. Sagemanifolds deals with differentiable manifolds of arbitrary dimension. Xrange yrange and zrange three tuples of the form var start stop giving the variables and.

A simple example is the velocity of a car that is traveling at 100 km h in a northerly direction. X 2sin y sqrt y 2 z exp x y log x y z 2. A vector field on is a function that assigns to each point a three dimensional vector. Three js has become the default viewer for 3d plots in replacement of jmol.

All this definition is saying is that a vector field is conservative if it is also a gradient vector field for some function. We usually represent a vector using an arrow. The basic objects are tensor fields and not tensor components in a given vector frame or coordinate chart. The size and direction.

Three js is the new default 3d viewer. A vector is a quantity with magnitude and direction.