(a) By jury. When trial by jury has been demanded as provided in Rule 38, the action shall be designated upon the register of actions as a jury action. The trial of all issues so demanded shall be by jury, unless

(a)(1) The parties or their attorneys of record, by written stipulation filed with the court or by an oral stipulation made in open court and entered in the record, consent to trial by the court sitting without a jury, or

(a)(2) The court upon motion or of its own initiative finds that a right of trial by jury of some or all of those issues does not exist, or

(a)(3) Either party to the issue fails to appear at the trial.

(b) By the court. Issues not demanded for trial by jury as provided in Rule 38 shall be tried by the court; but, notwithstanding the failure of a party to demand a jury in an action in which such a demand might have been made of right, the court in its discretion upon motion may order a trial by a jury of any or all issues.

(c) Advisory jury and trial by consent. In all actions not triable of right by a jury the court upon motion or of its own initiative may try any issue with an advisory jury or, with the consent of both parties, may order a trial with a jury whose verdict has the same effect as if trial by jury had been a matter of right.