У меня есть это исключение, и я неНе понимаю, почему это будет брошено или как я должен справиться с этим.

try {
    os.writeObject(element);
} catch (IOException e) {
    e.printStackTrace();
}

кудаelement этоTransformGroup содержащий некоторые другиеTransformGroups Экземпляр класса Atom:

public class Atom extends Group implements Serializable{
    float pozX,pozY;
    Group group= new Group();   
    Color3f blue = new Color3f(new Color(255));
    Color3f black = new Color3f(new Color(0));
    Sphere AtSph=new Sphere();

    public Atom(final float WEIGHT, final int BOUNDS,final float radius,Color3f color)
    {
        AppSetting ap= new AppSetting(color, black);
        AtSph=new Sphere(radius,1,100,ap);
    }
}

Полный журнал ошибок:

java.io.NotSerializableException: javax.media.j3d.TransformGroup
    at java.io.ObjectOutputStream.writeObject0(Unknown Source)
    at java.io.ObjectOutputStream.writeObject(Unknown Source)
    at cls.MolecularBuilder.addAtom(MolecularBuilder.java:511)
    at cls.MolecularBuilder$Console.HidrogenItemActionPerformed(MolecularBuilder.java:897)
    at cls.MolecularBuilder$Console$2.actionPerformed(MolecularBuilder.java:746)
    at javax.swing.AbstractButton.fireActionPerformed(Unknown Source)
    at javax.swing.AbstractButton$Handler.actionPerformed(Unknown Source)
    at javax.swing.DefaultButtonModel.fireActionPerformed(Unknown Source)
    at javax.swing.DefaultButtonModel.setPressed(Unknown Source)
    at javax.swing.AbstractButton.doClick(Unknown Source)
    at javax.swing.plaf.basic.BasicMenuItemUI.doClick(Unknown Source)
    at javax.swing.plaf.basic.BasicMenuItemUI$Handler.mouseReleased(Unknown Source)
    at java.awt.Component.processMouseEvent(Unknown Source)
    at javax.swing.JComponent.processMouseEvent(Unknown Source)
    at java.awt.Component.processEvent(Unknown Source)
    at java.awt.Container.processEvent(Unknown Source)
    at java.awt.Component.dispatchEventImpl(Unknown Source)
    at java.awt.Container.dispatchEventImpl(Unknown Source)
    at java.awt.Component.dispatchEvent(Unknown Source)
    at java.awt.LightweightDispatcher.retargetMouseEvent(Unknown Source)
    at java.awt.LightweightDispatcher.processMouseEvent(Unknown Source)
    at java.awt.LightweightDispatcher.dispatchEvent(Unknown Source)
    at java.awt.Container.dispatchEventImpl(Unknown Source)
    at java.awt.Window.dispatchEventImpl(Unknown Source)
    at java.awt.Component.dispatchEvent(Unknown Source)
    at java.awt.EventQueue.dispatchEventImpl(Unknown Source)
    at java.awt.EventQueue.access$200(Unknown Source)
    at java.awt.EventQueue$3.run(Unknown Source)
    at java.awt.EventQueue$3.run(Unknown Source)
    at java.security.AccessController.doPrivileged(Native Method)
    at java.security.ProtectionDomain$1.doIntersectionPrivilege(Unknown Source)
    at java.security.ProtectionDomain$1.doIntersectionPrivilege(Unknown Source)
    at java.awt.EventQueue$4.run(Unknown Source)
    at java.awt.EventQueue$4.run(Unknown Source)
    at java.security.AccessController.doPrivileged(Native Method)
    at java.security.ProtectionDomain$1.doIntersectionPrivilege(Unknown Source)
    at java.awt.EventQueue.dispatchEvent(Unknown Source)
    at java.awt.EventDispatchThread.pumpOneEventForFilters(Unknown Source)
    at java.awt.EventDispatchThread.pumpEventsForFilter(Unknown Source)
    at java.awt.EventDispatchThread.pumpEventsForHierarchy(Unknown Source)
    at java.awt.EventDispatchThread.pumpEvents(Unknown Source)
    at java.awt.EventDispatchThread.pumpEvents(Unknown Source)
    at java.awt.EventDispatchThread.run(Unknown Source)

Примечание. AppSetting (в классе Atom) - это просто пользовательский класс, расширяющий внешний вид.