The Ganesha yantra is drawn based on the teachings of Sri Narada in the ‘Ganesha dvadasanama stotra’. The twelve petal lotus is symbolic of the heart lotus and the door of this heart lotus is guarded by Ganesha.
This is the dancing form of Ganesha and the meditation etc, visualize Ganesha in a rather jovial, compromising mood. Ucchista Ganesha is worshiped to remove domestic disharmony and the relationship with spouse is improved. All sorts of troubles with in-laws etc vanish and the family gets together and lives happily. For the last two decades we have advised the placing of a statue of dancing Ganesha (idol) near the headstand of the bed and the relationship between couples has improved.
Sri Ganapati is the elephant headed son of Sri Shiva, belonging to the divine family that delivers the soul from darkness and sin, the specific function of Sri Ganapati is to teach and drive away ignorance (avidhya). He is represented by Ketu, the significator of emancipation from all kinds of bondage including rebirth.
The Beejakshara of Sri Ganapati is ‘gaM’
Bīja mantra: गं (gaṁ) which is also called the Gītā bīja (for Srimad Bhagavat Gītā) by those learned in mantra śāstra.
Contributed by Sarbani Rath
सनकाद्या मुनयो हनूमन्तं पप्रच्छुः।
आञ्जनेय महाबल तारकब्रह्मणो रामचन्द्रस्य
मन्त्रग्रामं नो ब्रूहीति।
sanakādyā munayo hanūmantaṁ papracchuḥ |
āñjaneya mahābala tārakabrahmaṇo rāmacandrasya
mantragrāmaṁ no brūhīti |
Translation: The saints headed by Sanaka again asked Hanūman: “Son of Āñjani of greatest strength, please speak the collection of Mantras for Tāraka-Brahmaṇa Rāmachandra.
वह्निस्थं शयनं विष्णोरर्धचन्द्रविभूषितम्।
एकाक्षरो मनुः प्रोक्तो मन्त्रराजः सुरद्रुमः॥ १॥
vahnisthaṁ śayanaṁ viṣṇorardhacandravibhūṣitam |
ekākṣaro manuḥ prokto mantrarājaḥ suradrumaḥ || 1||
Translation: fire (ra), śayana viṣṇu (ā) ardhacandra (ṁ) or rāṁ (राँ) is the one syllable mantra said by the wise to be
This opens a much bigger question that I have had: how should we actually define uttara-ayana. It seems that it was originally the winter solstice, where the days begin to get longer, but since it has become associated with Makara Saṅkrānti it has been riding a sidereal year, of which it is not really a sidereal calculation but a tropical calculation. If we truly are observing the Sun returning or the Sura increasing, then there is no relation to the signs, just actual ayanas (solstices).