What are the rules of the locative case?

Question

I understood the first time I heard about the locative that it was usually reserved for monosyllabic masculine nouns (ex. чай, дом, сок) with exceptions (кровь, дверь). However, I recently saw that на  дому is the correct usage for describing activities inside of a house, whereas на доме for activities on the roof.

But just today, I notice that the locative case isn't used once it is modified by an adjective? For example, I can find no record of the sentence на моём дому online, but instead, I see на моём доме. Are there any concrete rules to tell me when to use the locative, as what I am learning seems arbitrary.

Баян Купи-ка · Accepted Answer

But just today, I notice that the locative case isn't used once it is
  modified by an adjective?

Not quite, it's totally correct to say

На белом/рыхломadj. снегУ
  На крутомadj. валУ
  В горячемadj. боЮ
  В дремучемadj. лесУ
  На нашемposs. pron. векУ
  В новомadj. портУ
  В дальнемadj. краЮ
  В цветущемadj. садУ
  В липкомadj. потУ
  На своёмposs. pron. х..Ю
  В ночномadj. бредУ

I'd argue that дом is unique, because its Locative has only survived for  limited use in а particular sense of working from home. In fact despite being written separately на + дому, semantically it functions as an adverb (which are to be written jointly with prepositions), because it can answer not only the question where? but also how?, and this i believe is the reason for its reversal to Prepositional case once this fossilized semantic unity is broken up by insertion of intermediate words.

Randy Sanders · Answer

Hopefully, this will be helpful, I haven't studied the Russian Language for at least 45 years or so. But I found this on another page:
https://www.clozemaster.com/blog/russian-genitive-case/
However, Russian doesn’t like us to keep us too comfortable, so some of these partitive genitives have different forms than their normal run-of-the-mill genitives. These genitive forms are used with verbs, receptacles and indefinite numerals.
Nominative  Genitive singular (normal)  Partitive genitive  Translation  
лук         лука                        луку                onion  
сахар       сахара                      сахару              sugar  
чай         чая                         чаю                 tea  
суп         супа                        супу                soup  
табак       табака                      табаку              tobacco

This happens largely with masculine nouns ending in consonants.
Have fun with that!

Sergey Slepov · Answer

First of all, don't believe the other answers telling you that the locative is arbitrary and that there are no rules.
Locative is not arbitrary: for some words its use is required: в глазу, в боку, в саду; others (the majority) do not have a distinct locative form: в столе, в городе. It would be wrong to use them with the ending -у: в столу, в городу; and it would be wrong to say в глазе, в боке, в саде.

Are there any concrete rules to tell me when to use the locative?

Short answer: Yes, there are a few trends. Read the long answer.
Long answer:
In the course of the last few hundred years Locative (and Partitive) were gradually phased out of the language. Some words have lost their locatives completely. E.g. my granddad (born 1929) would say "в отпуску". Nowadays  this sounds peculiar, "в отпуске" is pretty much the only way of saying it.
Some words are "hesitating" (to various degrees): мозг, счёт (на вашем счёте/счету осталось...), аэропорт, цех, мост (дырка в мосте / в мосту):
Some have split meanings:

В углу комнаты лежит мяч.
В прямом угле 90 градусов.
На краю земли.
В Краснодарском крае.
В миру
В мире

Others have only kept locatives in set phrases: на нашем веку (vs в двадцатом веке), на виду (vs в нетрезвом виде), на дому (vs на доме), час (в пятом часу vs в одном часе 60 секунд).
You are not finding any examples of "на моём дому" because "на дому" is a set phrase.
Most high-frequency words continue to hold on to their locatives quite firmly: час, глаз, бок, лес, снег, берег...
There are a few towns / villages called "Сосновый бор" and "Старый мост". I'd really like to hear how those people describe where they live!

Quassnoi · Answer

Locative is pretty much arbitrary indeed.

To further complicate things, some of the words which technically have locative only use it in set phrases or in certain senses.

Дом is one of such words. While в дому still can be understood, it has long since fallen out of use in live Russian speech, and на дому is a set phrase meaning "at home" in the context of work: работа на дому means "outwork" and надомник means "outworker".

You can't really say на моём дому nowadays.

Other words like this are мир (в миру can only be used in the sense of "secular world"), щит (в щиту means "in the electric panel") and several others.

shabunc · Answer

There are no rules for locative cases but rather sporadic usages that are evidence of having locative (to some extent) earlier.

Usages of phrases like на дому, на снегу etc. should be memorized and that's it.

What are the rules of the locative case?

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