The Bhagavad-Dhyaana-Sopanam (literally "Steps in the Meditation on the Lord")
composed by Shri Vedanta Deshikan has 12 shlokas. Both in form and content, it
resembles ThiruppAnAzhwar's thamizh "amalanAdipirAn" verses and seems to be
inspired by it.
Shri N.Krishnamachari's summary of the shlokas is a good read.
The exploration here is to get at the meanings of each of the
words, investigate roots and related words.

[1] "Shri Desika Stotra Mala" by Shri Ramadesikachariar Swamy, 2003 Edition, Lifco
[2] "The Practical Sanskrit-English Dictionary" by Vaman Shivram Apte, Revised and Enlarged Edition, Motilal Banarsidass Pub
[3] Source: Bhagavad Dhyana Sopanam @ prapatti.com
[4] Shri V.Sadagopan's translations
[5] "A Sanskrit English Dictionary", M. Monier-Williams, Motilal Banarsidass Publishers
[6] Bhagavad Dhyana Sopanam commentary by Shri D. Ramaswamy Ayyangar

[Invocatory Tanian on Swami Desikan by Kumara Varadacharya]

    shrImAn ve~nkaTanAthAryaH   kavi-tArkika-kesarI
    vedAntAcArya-varyo me       saMnidhattAm sadA hR^idi

    
    
[01.txt]

    antarjyotiH kimapi yaminAm a~njanaM yoga-dR^iShTeH
        cintA-ratnaM sulabham iha naH siddhi-mokShAnurUpam
    dInAnAtha vyasana-shamanaM daivataM daivatAnAM
        divyaM cakShuH shruti-pariShadAM dR^iShyate ra~Nga-madhye

    

[02.txt]

    velAtIta-shruti-parimaLaM vedhasAM mauLi-sevyaM
        prAdurbhUtaM kanaka-saritaH saikate haMsa-juShTe
    lakShmI-bhUmyoH kara-sarasijairlAlitaM ra~Nga-bhartuH
        pAdAmbhojaM pratiphalati me bhAvanA-dIrghikAyAm

    

[03.txt]

    citrAkArAM kaTaka-rucibhishcAru vR^ittAnupUrvAM
        kAle dUtya drutataragatiM kAnti lIlA kalAcIm
    jAnucchAyA dviguNa-subhagAM ra~Nga-bharturmadAtmA
        ja~NghAM dR^iShTvA janana-padavI jA~NghikatvaM jahAti

    

[04.txt]

    kAmArAma-sthira-kadalikA-stambha-saMbhAvanIyaM
      kShaumAshliShTaM kimapi kamalA-bhUmi-nILopadhAnam
    nya~ncatkA~ncI-kiraNa-ruciraM nirvishatyUru-yugmaM
      lAvaNyaugha-dvayam iva matirmAmikA ra~Nga-yUnaH
         
    

[05.txt]

    saMprINAti pratikalam asau mAnasaM me sujAtA
      gambhIratvAt kvacana samaye gUDha-nikShipta-vishvA
    nAlIkena-sphurita-rajasA vedhaso nirmimANA
      ramyAvarta-dyuti-sahacarI ra~NganAthasya nAbhiH
    
    

[06.txt]

    shrIvatsena prathita-vibhavaM shrI-pada-nyAsa-dhanyaM
      madhyaM bAhvormaNivara-rucA ra~njitaM ra~Nga-dhAmnaH
    sAndracchAyaM taruNa-tulasI-citrayA vaijayantyA
      santApaM me shamayati dhiyashcandrikodAra-hAram
    
    

[07.txt]

    ekaM lIlopahitam itaraM bAhum AjAnu-lambaM
      prAptA ra~Nge-shayiturakhila-prArthanA-pArijAtam
    dR^iptA seyaM dR^iDha-niyamitA rashmibhirbhUShaNAnAM
      cintA-hastinyanubhavati me citram AlAna-yantram
        
    

[08.txt]

    sAbhiprAya-smita-vikasitaM cAru-bimbAdharoShThaM
      duHkhApAya-praNayini jane dUra-dattAbhimukhyam
    kAntaM vaktraM kanaka-tilakAla~NkR^itaM ra~Nga-bhartuH
      svAnte gADhaM mama vilagati svAgatodAra-netram

    

[09.txt]

    mAlyairantaH sthira-parimaLairvallabhA-sparsha-mAnyaiH
        kupyaccoLI vacana-kuTilaiH kuntalaiH shliShta-mUle
    ratnApIDa dyuti shabaLite ra~Nga-bhartuH kirITe
        rAjanvatyaH sthitim adhigatA vR^ittayashcetaso me
 
    
             
[10.txt]

    pAdAmbhojaM spR^ishati bhajate ra~NganAthasya ja~NghAM
        Urudvandve vilagati-shanair Urdhvam abhyeti nAbhim
    vakShasyAste valati bhujayormAmikeyaM manIShA
        vaktrAbhikhyAM pibati vahate vAsanAM mauLi-bandhe
         
    

[11.txt]

    kAntodArairayam iha bhujaiH ka~NkaNajyA kiNA~NkaiH
        lakShmI-dhAmnaH pR^ithula-paridhairlakShitAbhIti-hetiH
    agre kiMcit-bhujaga-shayanaH svAtmanaivAtmanaH san
        madhye ra~NgaM mama ca hR^idaye vartate sAvarodhaH

    

[12.txt]

    ra~NgAsthAne rasika-mahite ra~njitAsheSha-citte
        vidvatsevA vimala-manasA ve~NkaTeshena-kL^iptam
    akleshena-praNihita-dhiyAm ArurukShoravasthAM
        bhaktiM gADhAM dishatu bhagavad-dhyAna-sopAnam etat

    

[Valedictory Tanian on Swami Desikan by Kumara Varadacharya]

    kavi-tArkika-simhAya        kalyANa-guNa-shAline
    shrImate ve~nkaTeshAya      vedAnta-gurave namaH