jQuery conflict with MooTools

1. I have created slideoutmenu which pops out/in if I touch it/not with a cursor using MooTools: //MooTools, http://mootools.net, My Object Oriented (JavaScript) Tools. Copyright (c) 2006-2009 Valerio Proietti, http://mad4milk.net, MIT Style License. //core +FX.Scroll +Asset +event delegation

a part of my script:

window.addEvent('domready', function() {
new SlideoutMenu();



initialize: function()
{
    // FF2 Mac screws up the menu display. give the m the basic menu
    if (Browser.Platform.mac && Browser.Engine.gecko && Browser.Engine.version == 18) {
        $('menu').removeClass('js_live');
        return;
    }

    // iPhone should have normal menu
    if (Browser.Platform.ipod) {
        $('menu').removeClass('js_live');
        return;
    }

    this.bg_div = $('menu');
    this.menu_div = $$('#menu #opts')[0];

    this.logo_lnk = $$('#logo a')[0];
    if (this.logo_lnk.hasClass('home')) {
        this.is_homepage = true;
    }

    var rbsEasing = new Fx.Transition(Fx.Transitions.Expo, 4);      

    this.is_open = false;

    this.bgEffect = new Fx.Tween(this.bg_div, {
        unit: '%',
        property: 'width',
        duration: 650,
        transition: rbsEasing.easeOut,
        onComplete:this.bgEffectComplete.bind(this)
    });

    this.menuEffect = new Fx.Tween(this.menu_div, {
        property: 'left',
        transition: rbsEasing.easeOut,
        duration: 650
    });

    $('logo').addEvent('mouseenter', this.showMenu.bind(this));

    this.mouseBindCallback = this.moveMoveCallback.bind(this);
},

bgEffectComplete: function()
{
    if (this.is_open === false) {
        document.addEvent('mousemove', this.mouseBindCallback);
    }
    this.is_open = !this.is_open;
},

showMenu: function()
{
    if (this.is_open === true) {
        return;
    }

    this.bgEffect.start(70);
    this.menuEffect.start(600, $('logo').getPosition().x);

    this.logo_lnk.addClass('active');

    if (this.is_homepage) {
        this.logo_lnk.removeClass('home');
    }
},

hideMenu: function()
{
    this.bgEffect.start(0);
    this.menuEffect.start(600);

    this.logo_lnk.removeClass('active');

    if (this.is_homepage) {
        this.logo_lnk.addClass('home');
    }
},

moveMoveCallback: function(e)
{
    var close_right = this.menu_div.getPosition().x + 370;
    if (e.page.x > close_right && e.page.y > 80 && this.is_open === true) {
        document.removeEvent('mousemove', this.mouseBindCallback);
        this.hideMenu();
    }
}

The menu worked without any problem, then

1. I created a photo slideshow gallery using jquery and of course the menu stopped working. When I remove jquery it works fine again. There are many sites where it says that there is a conflict between javascript and jquery and it is not recommenced to use them together, though there is a solution with

   jQuery.noConflict(); which should be added after

Also I've changed $ with $j in mooTools file jsc.js and the one I created myself. Finally it worked but very weirdly, menu would pop out, but its elements were not aligned anymore and it wouldn't disappear when I moved the cursor away... I have a feeling there is a simple solution to this, it's because I lack of knowledge here I am asking for your help

never mind, solved it with

(function($){ /* your class files here */ })(document.id);