Is there a Mitzvah of Simcha applicable on Shabbos?
There is no Mitzvah of Simcha explicitly mentioned regarding Shabbos.
 Admur 529:8; and so is proven from 242:1 that Shabbos does not have a Mitzvah of Simcha. However, the Rebbe in Shaareiy Halacha Uminhag 1:127 writes that the reason that the Mitzvah of Simcha was not written regarding Shabbos is because it is nullified to the Mitzvah of Oneg applicable on Shabbos. However this requires further analysis as by Yom Tov there is also a Mitzvah of Oneg [Rabinically (529:5 as is the second opinion in 242:1), and if the Oneg involves Simcha-Biblically (242:1 KU”A 2)] and nonetheless Admur mentions also the Mitzvah of Simcha by Yom Tov. Thus, omitting the Mitzvah of Simcha by Shabbos seems to imply it does not exist, as writes Admur explicitly in 529:7.