## 22 Badges

16 years, 279 days

## Simple(?) algebra...

Maple 2017

This may be a frequently asked question but I could not find

it in MaplePrime's archives.

The expression

 > z := (x^(a+1) - x^a)/(x-1);

should simplify to . I don't know how to do that in Maple 2017.

I have tried all sorts of commands and assumption but none

worked.  For instance:

 > simplify(z) assuming x>1, a::posint;

What's the trick?

## How to model a bouncing ball through eve...

Maple

I wish to model the motion of a ball that bounces up and down in a vertical line, and whenever it hits the ground, it bounces back with only a fraction of the collision speed.

We expect that the amplitude of the consecutive bounces to diminish and for all practical purposes the ball to come to a standstill.  It's not difficult to calculate the motion analytically by hand.

However, when I attempted to solve the equation of motion numerically with Maple's dsolve()  and event handling, I ran into a problem.  As the amplitude of the bounces approaches zero, numerical noise sets in and the ball tunnels itself underground!  See the worksheet below.

I don't know how to prevent the ball from going underground.  Any ideas?

 > restart;
 > de := diff(y(t),t,t)=-1;

 > ic := y(0)=1, D(y)(0)=0;

 > Events := [y(t)=0, diff(y(t),t)=-0.5*diff(y(t),t)];

 > dsol := dsolve({de, ic}, numeric,                  events=[Events], range=0..5);

 > plots[odeplot](dsol, thickness=3, color=red);

Download bouncing_ball.mw

## 3D globe for Maple?...

Maple

Is there a 3D globe available for Maple?  Specifically, a globe depicting the Earth's continents and oceans, that can be grabbed and rotated with the mouse like any other 3D Maple plot?

## Unexpected convert...

Maple 2017

This behavior seems rather odd.  Is it documented anywhere?

 > v := ;
 > a := 3: b := 4:
 > v;
 > convert(v, list);

I expected that final result to be [3,4].  Why is it [a,b]?

I know that I can do eval(convert(v, list)) to get the numerical value, but why is the eval necessary?

## How to convert arctan to arcsin?...

Maple

I am stumped with this trivial puzzle.  Let
z := arctan(x/sqrt(a^2-x^2));

How do we simplify z to.

I tried all sorts of tricks with simplify(...) and convert(...), with assumptions, but did not get anywhere.  Any clues?

Versions: Maple 2016 and 2017.

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